Maths-
General
Easy

Question

Write 3.4 cross times 10 to the power of negative 6 end exponent In a standard form.

Hint:

Check whether power of 10 is positive or negative, then move the
decimal places and write the standard form.

The correct answer is: 0.0000034


    Complete step by step solution:
    Here we have 3.4 cross times 10 to the power of negative 6 end exponent as the number.
    Because of the exponent of 10s term is negative, we must move the decimal 6 places to the left.
    So we get, 3.4 cross times 10 to the power of negative 6 end exponent equals 0.0000034 as the standard from.

    Related Questions to study

    General
    Maths-

    Express 586000000 in scientific notation

    Complete step by step solution:
    Here we have the number to be  586000000
    Take the number and move a decimal place to the right one position.
    So we get 5.86000000
    Now we have 8 places to the right of the decimal.
    This can be expressed as 5.86 cross times 10 to the power of 8

    Express 586000000 in scientific notation

    Maths-General
    Complete step by step solution:
    Here we have the number to be  586000000
    Take the number and move a decimal place to the right one position.
    So we get 5.86000000
    Now we have 8 places to the right of the decimal.
    This can be expressed as 5.86 cross times 10 to the power of 8
    General
    Maths-

    Express 0.00000000002985 as a single digit times a power of ten rounded to the nearest ten millionth?

    Complete step by step solution:
    Here the digit given is 0.00000000002985.
    Here we have 0 in the ten millionth place value and 0 in the hundred millionth place value.
    Since we have zeros in all these positions, we get rounded values also as zero

    Express 0.00000000002985 as a single digit times a power of ten rounded to the nearest ten millionth?

    Maths-General
    Complete step by step solution:
    Here the digit given is 0.00000000002985.
    Here we have 0 in the ten millionth place value and 0 in the hundred millionth place value.
    Since we have zeros in all these positions, we get rounded values also as zero
    General
    Maths-

    The Population of cities A and B are 2.6 cross times 10 to the power of 5 and 1560,000respectively. The population of city C is twice the population of city B. The population of city C is how many times the population of city A ?

    Complete step by step solution:
    Population of city A = 2.6 cross times 10 to the power of 5
    Population of city B = 1560000 = 15.6 cross times 10 to the power of 5
    Population of city C = 2cross times1560000 = 2 cross times 15.6 cross times 10 to the power of 5
    On dividing population of city C by population of city A, we have fraction numerator 2 cross times 15.6 cross times 10 to the power of 5 over denominator 2.6 cross times 10 to the power of 5 end fraction
    On cancelling  on numerator and denominator, we have
    not stretchy rightwards double arrow fraction numerator 2 cross times 15.6 over denominator 2.6 end fraction equals 12
    Hence the population of city C is 12 times the population of city A.

    The Population of cities A and B are 2.6 cross times 10 to the power of 5 and 1560,000respectively. The population of city C is twice the population of city B. The population of city C is how many times the population of city A ?

    Maths-General
    Complete step by step solution:
    Population of city A = 2.6 cross times 10 to the power of 5
    Population of city B = 1560000 = 15.6 cross times 10 to the power of 5
    Population of city C = 2cross times1560000 = 2 cross times 15.6 cross times 10 to the power of 5
    On dividing population of city C by population of city A, we have fraction numerator 2 cross times 15.6 cross times 10 to the power of 5 over denominator 2.6 cross times 10 to the power of 5 end fraction
    On cancelling  on numerator and denominator, we have
    not stretchy rightwards double arrow fraction numerator 2 cross times 15.6 over denominator 2.6 end fraction equals 12
    Hence the population of city C is 12 times the population of city A.
    parallel
    General
    Maths-

    The length of plant cell A is  meter. The length of plant cell B is 0.000004 meter. How many times greater is plant cell A’s length than plant cell B’s length.

    Complete step by step solution:
    Length of plant A cell = 8 cross times 10 to the power of negative 5 end exponent equals 0.00008 straight m
    Length of plant B cell = 0.000004m
    On dividing length of plant A by plant B, we have fraction numerator 0.00008 over denominator 0.000004 end fraction
    not stretchy rightwards double arrow fraction numerator 80 cross times 10 to the power of negative 6 end exponent over denominator 4 cross times 10 to the power of negative 6 end exponent end fraction (write both numerator and denominator as same powers of base 10)
    On cancelling 10-6 on numerator and denominator, we have
    not stretchy rightwards double arrow 80 over 4 equals 20
    Hence, the length of plant A cell is 20 times greater than the length of plant B cell.

    The length of plant cell A is  meter. The length of plant cell B is 0.000004 meter. How many times greater is plant cell A’s length than plant cell B’s length.

    Maths-General
    Complete step by step solution:
    Length of plant A cell = 8 cross times 10 to the power of negative 5 end exponent equals 0.00008 straight m
    Length of plant B cell = 0.000004m
    On dividing length of plant A by plant B, we have fraction numerator 0.00008 over denominator 0.000004 end fraction
    not stretchy rightwards double arrow fraction numerator 80 cross times 10 to the power of negative 6 end exponent over denominator 4 cross times 10 to the power of negative 6 end exponent end fraction (write both numerator and denominator as same powers of base 10)
    On cancelling 10-6 on numerator and denominator, we have
    not stretchy rightwards double arrow 80 over 4 equals 20
    Hence, the length of plant A cell is 20 times greater than the length of plant B cell.
    General
    Maths-

    Krishan made 43,875 last year . use a single digit times a power of ten to express this value rounded to the nearest ten thousand.

    Complete step by step solution:
    Here the digit given is 43,875.
    Check the number immediately right of the number in the ten thousandth place.
    Here we have 3 in that position.
    Since 3 < 5,  we keep the number in ten thousands place the same and change all
    of the numbers that follow, to zeros.
    So here, we get 43875 rounded to the nearest 10000th is 40000.
    This can be expressed as 4 cross times 104

    Krishan made 43,875 last year . use a single digit times a power of ten to express this value rounded to the nearest ten thousand.

    Maths-General
    Complete step by step solution:
    Here the digit given is 43,875.
    Check the number immediately right of the number in the ten thousandth place.
    Here we have 3 in that position.
    Since 3 < 5,  we keep the number in ten thousands place the same and change all
    of the numbers that follow, to zeros.
    So here, we get 43875 rounded to the nearest 10000th is 40000.
    This can be expressed as 4 cross times 104
    General
    Maths-

    Which is greater 6 cross times 10 to the power of negative 6 end exponent and 2 cross times 10 to the power of negative 8 end exponent

    Complete step by step solution:
    Here 6 cross times 10 to the power of negative 6 end exponent can be written as 0.000006
    Because of the exponent of 10s term is negative, we must move the decimal 6
    places to the left and
    2 cross times 10 to the power of negative 8 end exponent can be written as 0.00000002
    Because of the exponent of 10s term is negative, we must move the decimal 8
    places to the left.
    Here it is clear that 0.000006 > 0.00000002
    That is, 6 cross times 10 to the power of negative 6 end exponent greater than 2 cross times 10 to the power of negative 8 end exponent
     

    Which is greater 6 cross times 10 to the power of negative 6 end exponent and 2 cross times 10 to the power of negative 8 end exponent

    Maths-General
    Complete step by step solution:
    Here 6 cross times 10 to the power of negative 6 end exponent can be written as 0.000006
    Because of the exponent of 10s term is negative, we must move the decimal 6
    places to the left and
    2 cross times 10 to the power of negative 8 end exponent can be written as 0.00000002
    Because of the exponent of 10s term is negative, we must move the decimal 8
    places to the left.
    Here it is clear that 0.000006 > 0.00000002
    That is, 6 cross times 10 to the power of negative 6 end exponent greater than 2 cross times 10 to the power of negative 8 end exponent
     
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    General
    Maths-

    Estimate 0.037854921 to the nearest hundredth. Express your answer as a single digit times a power 10 ?
     

    Complete step by step solution:
    Here the digit at the thousandth place in the given decimal number is 7.
    Since 7 > 5,  we add 1 to the digit at the hundredth place and remove all the
    digits right to it.
    So here, we get 0.037854921 rounded to the nearest 100th is 0.04.
    This can be expressed as 4 cross times 10-2

    Estimate 0.037854921 to the nearest hundredth. Express your answer as a single digit times a power 10 ?
     

    Maths-General
    Complete step by step solution:
    Here the digit at the thousandth place in the given decimal number is 7.
    Since 7 > 5,  we add 1 to the digit at the hundredth place and remove all the
    digits right to it.
    So here, we get 0.037854921 rounded to the nearest 100th is 0.04.
    This can be expressed as 4 cross times 10-2
    General
    Maths-

    Sita estimated 30490000000000 as 3 x 108 , What error did she make ?

    Complete step by step solution:
    Here we have  30490000000000 as the number
    We have 10 zeros after 3049,
    hence we can write 30490000000000 as 3049 cross times 10 to the power of 10

    Sita estimated 30490000000000 as 3 x 108 , What error did she make ?

    Maths-General
    Complete step by step solution:
    Here we have  30490000000000 as the number
    We have 10 zeros after 3049,
    hence we can write 30490000000000 as 3049 cross times 10 to the power of 10
    General
    Maths-

    Write the standard form for 6.8 cross times 10 to the power of negative 8 end exponent

    Complete step by step solution:
    Here, 6.8 cross times 10 to the power of negative 8 end exponent equals 0.000000068
    Because of the exponent of 10s term is negative, we must move the decimal 8
    places to the left.

    Write the standard form for 6.8 cross times 10 to the power of negative 8 end exponent

    Maths-General
    Complete step by step solution:
    Here, 6.8 cross times 10 to the power of negative 8 end exponent equals 0.000000068
    Because of the exponent of 10s term is negative, we must move the decimal 8
    places to the left.
    parallel
    General
    Maths-

    Simplify by combining similar terms: 2 root index 8 of 4 plus 7 cube root of 32 minus cube root of 500

    Complete step by step solution:
    Here we can write, 2 cube root of 4 equals 2 cross times 4 to the power of 1 third end exponent comma 7 root index 8 of 32 equals 7 cross times 32 to the power of 1 third end exponent and cube root of 500 equals 500 to the power of 1 third end exponent
    This can be written as 2 cross times 2 to the power of 2 to the power of 1 third end exponent end exponent comma 7 cross times 2 to the power of 5 to the power of 1 third end exponent end exponent text  and  end text open parentheses 2 squared cross times 5 cubed close parentheses to the power of 1 third end exponent
    So, 2 cube root of 4 plus 7 cube root of 32 minus cube root of 500 equals 2 cross times 2 to the power of 2 over 3 end exponent plus 7 cross times 2 to the power of 5 over 3 end exponent minus 5 cross times 2 to the power of 2 over 3 end exponent
    Taking common term 2 to the power of 2 over 3 end exponent outside, we have 2 to the power of 2 over 3 end exponent open parentheses 2 plus 7 cross times 2 to the power of 3 over 3 end exponent minus 5 close parentheses
    table attributes columnspacing 1em end attributes row cell not stretchy rightwards double arrow 2 to the power of 2 over 3 end exponent open parentheses 2 plus 7 cross times 2 minus 5 close parentheses end cell row cell not stretchy rightwards double arrow 2 to the power of 2 over 3 end exponent left parenthesis 11 right parenthesis end cell end table

    Simplify by combining similar terms: 2 root index 8 of 4 plus 7 cube root of 32 minus cube root of 500

    Maths-General
    Complete step by step solution:
    Here we can write, 2 cube root of 4 equals 2 cross times 4 to the power of 1 third end exponent comma 7 root index 8 of 32 equals 7 cross times 32 to the power of 1 third end exponent and cube root of 500 equals 500 to the power of 1 third end exponent
    This can be written as 2 cross times 2 to the power of 2 to the power of 1 third end exponent end exponent comma 7 cross times 2 to the power of 5 to the power of 1 third end exponent end exponent text  and  end text open parentheses 2 squared cross times 5 cubed close parentheses to the power of 1 third end exponent
    So, 2 cube root of 4 plus 7 cube root of 32 minus cube root of 500 equals 2 cross times 2 to the power of 2 over 3 end exponent plus 7 cross times 2 to the power of 5 over 3 end exponent minus 5 cross times 2 to the power of 2 over 3 end exponent
    Taking common term 2 to the power of 2 over 3 end exponent outside, we have 2 to the power of 2 over 3 end exponent open parentheses 2 plus 7 cross times 2 to the power of 3 over 3 end exponent minus 5 close parentheses
    table attributes columnspacing 1em end attributes row cell not stretchy rightwards double arrow 2 to the power of 2 over 3 end exponent open parentheses 2 plus 7 cross times 2 minus 5 close parentheses end cell row cell not stretchy rightwards double arrow 2 to the power of 2 over 3 end exponent left parenthesis 11 right parenthesis end cell end table
    General
    Maths-

    Evaluate x squared plus 1 over x squared text  if  end text x equals 3 plus square root of 8

    Complete step by step solution:
    Let x equals 3 plus square root of 8
    ∴ 1 over x equals fraction numerator 1 over denominator 3 plus square root of 8 end fraction equals fraction numerator 1 cross times 3 minus square root of 8 over denominator left parenthesis 3 plus square root of 8 right parenthesis left parenthesis 3 minus square root of 8 right parenthesis end fraction (Rationalising the denominator)
    table attributes columnspacing 1em end attributes row cell equals fraction numerator 3 minus square root of 8 over denominator left parenthesis 3 right parenthesis squared minus left parenthesis square root of 8 right parenthesis squared end fraction equals fraction numerator 3 minus square root of 8 over denominator 9 minus 8 end fraction equals fraction numerator 3 minus square root of 8 over denominator 1 end fraction end cell row cell equals 3 minus square root of 8 end cell end table
    Now, x plus 1 over x equals 3 plus square root of 8 plus 3 minus square root of 8 equals 6
    Squaring both sides, we get open parentheses x plus 1 over x close parentheses squared equals 6 squared
    not stretchy rightwards double arrow x squared plus 1 over x squared plus 2 equals 36
    not stretchy rightwards double arrow x squared plus 1 over x squared equals 36 minus 2 equals 34

    Evaluate x squared plus 1 over x squared text  if  end text x equals 3 plus square root of 8

    Maths-General
    Complete step by step solution:
    Let x equals 3 plus square root of 8
    ∴ 1 over x equals fraction numerator 1 over denominator 3 plus square root of 8 end fraction equals fraction numerator 1 cross times 3 minus square root of 8 over denominator left parenthesis 3 plus square root of 8 right parenthesis left parenthesis 3 minus square root of 8 right parenthesis end fraction (Rationalising the denominator)
    table attributes columnspacing 1em end attributes row cell equals fraction numerator 3 minus square root of 8 over denominator left parenthesis 3 right parenthesis squared minus left parenthesis square root of 8 right parenthesis squared end fraction equals fraction numerator 3 minus square root of 8 over denominator 9 minus 8 end fraction equals fraction numerator 3 minus square root of 8 over denominator 1 end fraction end cell row cell equals 3 minus square root of 8 end cell end table
    Now, x plus 1 over x equals 3 plus square root of 8 plus 3 minus square root of 8 equals 6
    Squaring both sides, we get open parentheses x plus 1 over x close parentheses squared equals 6 squared
    not stretchy rightwards double arrow x squared plus 1 over x squared plus 2 equals 36
    not stretchy rightwards double arrow x squared plus 1 over x squared equals 36 minus 2 equals 34
    General
    Maths-

    Simplify 4√12+5√27 - 3√75 +√300

    Complete step by step solution:
    On prime factorization, we can write
    4 square root of 12 equals 4 cross times square root of 2 cross times 2 cross times 3 end root comma 5 square root of 27 equals 5 cross times square root of 3 cross times 3 cross times 3 end root comma 3 square root of 75 equals 3 cross times square root of 3 cross times 5 cross times 5 end root
    and square root of 300 equals square root of 2 cross times 2 cross times 3 cross times 5 cross times 5 end root
    This can be written as 8 square root of 3 comma 15 square root of 3 comma 15 square root of 3 and 10 square root of 3 respectively.
    So, 4 square root of 12 plus 5 square root of 27 minus 3 square root of 75 plus square root of 300 equals 8 square root of 3 plus 15 square root of 3 minus 15 square root of 3 plus 10 square root of 3 equals 18 square root of 3

    Simplify 4√12+5√27 - 3√75 +√300

    Maths-General
    Complete step by step solution:
    On prime factorization, we can write
    4 square root of 12 equals 4 cross times square root of 2 cross times 2 cross times 3 end root comma 5 square root of 27 equals 5 cross times square root of 3 cross times 3 cross times 3 end root comma 3 square root of 75 equals 3 cross times square root of 3 cross times 5 cross times 5 end root
    and square root of 300 equals square root of 2 cross times 2 cross times 3 cross times 5 cross times 5 end root
    This can be written as 8 square root of 3 comma 15 square root of 3 comma 15 square root of 3 and 10 square root of 3 respectively.
    So, 4 square root of 12 plus 5 square root of 27 minus 3 square root of 75 plus square root of 300 equals 8 square root of 3 plus 15 square root of 3 minus 15 square root of 3 plus 10 square root of 3 equals 18 square root of 3
    parallel
    General
    Maths-

    Simplify √45 - 3√20 +4√5

    Complete step by step solution:
    On prime factorization, we can write
    square root of 45 equals square root of 3 cross times 3 cross times 5 end root comma 3 square root of 20 equals 3 cross times square root of 2 cross times 2 cross times 5 end root text  and  end text 4 square root of 5 equals 4 square root of 5
    This can be written as 3 square root of 5 comma 6 square root of 5 and 4 square root of 5 respectively.
    So, square root of 45 minus 3 square root of 20 plus 4 square root of 5 equals 3 square root of 5 minus 6 square root of 5 plus 4 square root of 5 equals 1 square root of 5 equals square root of 5

    Simplify √45 - 3√20 +4√5

    Maths-General
    Complete step by step solution:
    On prime factorization, we can write
    square root of 45 equals square root of 3 cross times 3 cross times 5 end root comma 3 square root of 20 equals 3 cross times square root of 2 cross times 2 cross times 5 end root text  and  end text 4 square root of 5 equals 4 square root of 5
    This can be written as 3 square root of 5 comma 6 square root of 5 and 4 square root of 5 respectively.
    So, square root of 45 minus 3 square root of 20 plus 4 square root of 5 equals 3 square root of 5 minus 6 square root of 5 plus 4 square root of 5 equals 1 square root of 5 equals square root of 5
    General
    Maths-

    Arrange in ascending order of magnitude square root of 5 comma root index 8 of 11 and 2 root index 6 of 3

    Complete step by step solution:
    Here we can write, square root of 5 equals 5 to the power of 1 half end exponent comma root index 8 of 11 equals 11 to the power of 1 third end exponent text  and  end text 2 root index 6 of 3 equals root index 6 of 12 equals 12 to the power of 1 over 6 end exponent
    On taking the LCM of 2,3,6 we have LCM as 6.
    So, not stretchy rightwards double arrow 5 to the power of 1 half end exponent equals 5 to the power of fraction numerator 1 cross times 3 over denominator 2 cross times 3 end fraction end exponent equals 5 to the power of 3 over 6 end exponent
    not stretchy rightwards double arrow open parentheses 5 cubed close parentheses to the power of 1 over 6 end exponent equals 125 to the power of 1 over 6 end exponent space of 1em open parentheses text  Since  end text open parentheses a to the power of b close parentheses to the power of c equals a to the power of b c end exponent close parentheses
    Likewise, not stretchy rightwards double arrow 11 to the power of 1 third end exponent equals 11 to the power of fraction numerator 1 cross times 2 over denominator 3 cross times 2 end fraction end exponent equals 11 to the power of 2 over 6 end exponent
    not stretchy rightwards double arrow open parentheses 11 squared close parentheses to the power of 1 over 6 end exponent equals 121 to the power of 1 over 6 end exponent space of 1em open parentheses text  Since  end text open parentheses a to the power of b close parentheses to the power of c equals a to the power of b c end exponent close parentheses
    Likewise, not stretchy rightwards double arrow 12 to the power of 1 over 6 end exponent
    Now, we have 125 to the power of 1 over 6 end exponent comma 121 to the power of 1 over 6 end exponent and 12 to the power of 1 over 6 end exponent
    So, here ascending order is 12 < 121 < 125
    not stretchy rightwards double arrow 12 to the power of 1 over 6 end exponent less than 121 to the power of 1 over 6 end exponent less than 125 to the power of 1 over 6 end exponent
    table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell not stretchy rightwards double arrow 12 to the power of 1 over 6 end exponent less than 11 to the power of 1 third end exponent less than 5 to the power of 1 half end exponent end cell row cell not stretchy rightwards double arrow root index 6 of 12 less than cube root of 11 less than square root of 5 end cell end table

    Arrange in ascending order of magnitude square root of 5 comma root index 8 of 11 and 2 root index 6 of 3

    Maths-General
    Complete step by step solution:
    Here we can write, square root of 5 equals 5 to the power of 1 half end exponent comma root index 8 of 11 equals 11 to the power of 1 third end exponent text  and  end text 2 root index 6 of 3 equals root index 6 of 12 equals 12 to the power of 1 over 6 end exponent
    On taking the LCM of 2,3,6 we have LCM as 6.
    So, not stretchy rightwards double arrow 5 to the power of 1 half end exponent equals 5 to the power of fraction numerator 1 cross times 3 over denominator 2 cross times 3 end fraction end exponent equals 5 to the power of 3 over 6 end exponent
    not stretchy rightwards double arrow open parentheses 5 cubed close parentheses to the power of 1 over 6 end exponent equals 125 to the power of 1 over 6 end exponent space of 1em open parentheses text  Since  end text open parentheses a to the power of b close parentheses to the power of c equals a to the power of b c end exponent close parentheses
    Likewise, not stretchy rightwards double arrow 11 to the power of 1 third end exponent equals 11 to the power of fraction numerator 1 cross times 2 over denominator 3 cross times 2 end fraction end exponent equals 11 to the power of 2 over 6 end exponent
    not stretchy rightwards double arrow open parentheses 11 squared close parentheses to the power of 1 over 6 end exponent equals 121 to the power of 1 over 6 end exponent space of 1em open parentheses text  Since  end text open parentheses a to the power of b close parentheses to the power of c equals a to the power of b c end exponent close parentheses
    Likewise, not stretchy rightwards double arrow 12 to the power of 1 over 6 end exponent
    Now, we have 125 to the power of 1 over 6 end exponent comma 121 to the power of 1 over 6 end exponent and 12 to the power of 1 over 6 end exponent
    So, here ascending order is 12 < 121 < 125
    not stretchy rightwards double arrow 12 to the power of 1 over 6 end exponent less than 121 to the power of 1 over 6 end exponent less than 125 to the power of 1 over 6 end exponent
    table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell not stretchy rightwards double arrow 12 to the power of 1 over 6 end exponent less than 11 to the power of 1 third end exponent less than 5 to the power of 1 half end exponent end cell row cell not stretchy rightwards double arrow root index 6 of 12 less than cube root of 11 less than square root of 5 end cell end table
    General
    Maths-

    The Diagonals of a square ABCD meet at O. Prove that A B squared equals 2 A O squared


    Aim  :- Prove that AB squared equals 2 AO squared


    Let length of side of square be a
    Then ,applying using pythagoras theorem in triangle ADC
    We get A C squared equals A D squared plus D C squared not stretchy rightwards double arrow A C squared equals a squared plus a squared
    not stretchy rightwards double arrow AC squared equals 2 straight a squared
    As diagonals bisect each other AC = 2OA
    20 straight A squared equals straight a squared where a =AB
    We get AB squared equals 2 AO squared
    Hence proved

    The Diagonals of a square ABCD meet at O. Prove that A B squared equals 2 A O squared

    Maths-General

    Aim  :- Prove that AB squared equals 2 AO squared


    Let length of side of square be a
    Then ,applying using pythagoras theorem in triangle ADC
    We get A C squared equals A D squared plus D C squared not stretchy rightwards double arrow A C squared equals a squared plus a squared
    not stretchy rightwards double arrow AC squared equals 2 straight a squared
    As diagonals bisect each other AC = 2OA
    20 straight A squared equals straight a squared where a =AB
    We get AB squared equals 2 AO squared
    Hence proved

    parallel

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