Maths-
General
Easy

Question

Express 0.5248 in the lowest form.

Hint:

Make the decimal into a proper fraction and then find the lowest form.

The correct answer is: 0.5248


    Complete step by step solution:
    0.5248 can be written as fraction numerator 0.5248 over denominator 1 end fraction
    Here, we have 4 decimals.
    On multiplying numerator and denominator by 10000, we get
    fraction numerator 0.5248 over denominator 1 end fraction equals 5248 over 10000
    On simplifications, we have
    5248 over 10000 equals fraction numerator 328 cross times 16 over denominator 625 cross times 16 end fraction equals 328 over 625
    So 328 over 625 is the lowest form of 0.5248

    Related Questions to study

    General
    Maths-

    Write the following numbers in the scientific notation : 0.00000000065

    Hint:-
    1. In Mathematics, lets say, "a" represents a number and "n" is the number of times that number is to be multiplied with itself, in order to get a desired result. Then, such result can be written as an, where a is called the base and n is its power/ exponent.
    an = a × a × ... × a                  n times.
    2. A number is written in scientific notation when a number between 1 and 10 is multiplied by a power of 10.
    0.00000000065
    = 6.5 × 10-10 …............................ (We shifted the decimal 10 places to the right to get a number between 1 and 10)
    Final Answer:-
    The given expressions can be written in their scientific notation as  6.5 × 10-10.

    Write the following numbers in the scientific notation : 0.00000000065

    Maths-General
    Hint:-
    1. In Mathematics, lets say, "a" represents a number and "n" is the number of times that number is to be multiplied with itself, in order to get a desired result. Then, such result can be written as an, where a is called the base and n is its power/ exponent.
    an = a × a × ... × a                  n times.
    2. A number is written in scientific notation when a number between 1 and 10 is multiplied by a power of 10.
    0.00000000065
    = 6.5 × 10-10 …............................ (We shifted the decimal 10 places to the right to get a number between 1 and 10)
    Final Answer:-
    The given expressions can be written in their scientific notation as  6.5 × 10-10.
    General
    Maths-

    Write the following numbers in the scientific notation : a) 5,07,460000000

    Hint:-
    1. In Mathematics, lets say, "a" represents a number and "n" is the number of times that number is to be multiplied with itself, in order to get a desired result. Then, such result can be written as an, where a is called the base and n is its power/ exponent.
    an = a × a × ... × a             n times.
    2. A number is written in scientific notation when a number between 1 and 10 is multiplied by a power of 10.
    Step-by-step solution:-
    a) 5,07,460000000.00
    = 5.07460000000 × 1011 …................ (We shifted the decimal 11 places towards the left to get a number between 1 and 10)
    = 5.0746 × 1011
    Final Answer:-
    ∴ The given expressions can be written in their scientific notation as 5.0746 × 1011

    Write the following numbers in the scientific notation : a) 5,07,460000000

    Maths-General
    Hint:-
    1. In Mathematics, lets say, "a" represents a number and "n" is the number of times that number is to be multiplied with itself, in order to get a desired result. Then, such result can be written as an, where a is called the base and n is its power/ exponent.
    an = a × a × ... × a             n times.
    2. A number is written in scientific notation when a number between 1 and 10 is multiplied by a power of 10.
    Step-by-step solution:-
    a) 5,07,460000000.00
    = 5.07460000000 × 1011 …................ (We shifted the decimal 11 places towards the left to get a number between 1 and 10)
    = 5.0746 × 1011
    Final Answer:-
    ∴ The given expressions can be written in their scientific notation as 5.0746 × 1011
    General
    Maths-

    A town has about 25,00 people living in it and the mayor wants to send each person 10,00 as a celebration gift because the town won the Federal Lottery for Small Towns. How much money would the town need to give out this celebration gift?

    Hint:-
    1. In Mathematics, lets say, "a" represents a number and "n" is the number of times that number is to be multiplied with itself, in order to get a desired result. Then, such result can be written as an, where a is called the base and n is its power/ exponent.
    an = a × a × ... × a                       n times.
    2. Total Amount required = Number of people living in the town × Amount required for each person.
    Step-by-step solution:-
    Number of people living in the town = 2500 ….................................. (Equation i)
    Amount required for each person = 1000 …...................................... (Equation ii)
    Now, we know that-
    Total Amount required = Number of people living in the town × Amount required for each person
    ∴ Total Amount required = 2500 × 1000 ........................................... (From Equations i & ii)
    ∴ Total Amount required = 25,00,000
    Final Answer:-
    ∴ The town needs 25,00,000 units of its currency to give out this celebration gift.

    A town has about 25,00 people living in it and the mayor wants to send each person 10,00 as a celebration gift because the town won the Federal Lottery for Small Towns. How much money would the town need to give out this celebration gift?

    Maths-General
    Hint:-
    1. In Mathematics, lets say, "a" represents a number and "n" is the number of times that number is to be multiplied with itself, in order to get a desired result. Then, such result can be written as an, where a is called the base and n is its power/ exponent.
    an = a × a × ... × a                       n times.
    2. Total Amount required = Number of people living in the town × Amount required for each person.
    Step-by-step solution:-
    Number of people living in the town = 2500 ….................................. (Equation i)
    Amount required for each person = 1000 …...................................... (Equation ii)
    Now, we know that-
    Total Amount required = Number of people living in the town × Amount required for each person
    ∴ Total Amount required = 2500 × 1000 ........................................... (From Equations i & ii)
    ∴ Total Amount required = 25,00,000
    Final Answer:-
    ∴ The town needs 25,00,000 units of its currency to give out this celebration gift.
    parallel
    General
    Maths-

    The temperature halfway to the Sun from venus is approximately 1,800° c and scientists theorize that it may be up to 26,000 times hotter at the center of the Sun. Approximately how hot is it at the center of the Sun?

    Hint:-
    In Mathematics, lets say, "a" represents a number and "n" is the number of times that number is to be multiplied with itself, in order to get a desired result. Then, such result can be written as an, where a is called the base and n is its power/ exponent.
    an = a × a × ... × a                  n times.
    Step-by-step solution:-
    Temperature at the centre of the sun = Temperature halfway to the sun × 26,000 ….................... (As per given information)
    ∴ Temperature at the centre of the sun = 1,800° c × 26,000
    ∴ Temperature at the centre of the sun = 4,68,00,000° c
    or Temperature at the centre of the sun = (4.68 × 107)° c
    Final Answer:-
    ∴ Temperature at the centre of the sun is approximately- (4.68 × 107)° c or 4,68,00,000° c

    The temperature halfway to the Sun from venus is approximately 1,800° c and scientists theorize that it may be up to 26,000 times hotter at the center of the Sun. Approximately how hot is it at the center of the Sun?

    Maths-General
    Hint:-
    In Mathematics, lets say, "a" represents a number and "n" is the number of times that number is to be multiplied with itself, in order to get a desired result. Then, such result can be written as an, where a is called the base and n is its power/ exponent.
    an = a × a × ... × a                  n times.
    Step-by-step solution:-
    Temperature at the centre of the sun = Temperature halfway to the sun × 26,000 ….................... (As per given information)
    ∴ Temperature at the centre of the sun = 1,800° c × 26,000
    ∴ Temperature at the centre of the sun = 4,68,00,000° c
    or Temperature at the centre of the sun = (4.68 × 107)° c
    Final Answer:-
    ∴ Temperature at the centre of the sun is approximately- (4.68 × 107)° c or 4,68,00,000° c
    General
    Maths-

    A state has an area of approximately 9,604,100,000 square miles and has approximately 110,000 people. How much area is this per person?

    Hint:-
    1. In Mathematics, lets say, "a" represents a number and "n" is the number of times that number is to be multiplied with itself, in order to get a desired result. Then, such result can be written as an, where a is called the base and n is its power/ exponent.
    an = a × a × ... × a             n times.
    2. Total Area = Number of people living in the area × Area per person.
    Step-by-step solution:-
    Total Area = 9604100000 sq. miles …................................................ (Equation i)
    Number of people living in the area = 110000 …............................. (Equation ii)
    Now, we know that-
    Total Area = Number of people living in the area × Area per person
    ∴ 9604100000 = 110000 × Area per person
    ∴ 9604100000 / 110000 = Area per person
    ∴ 87,310 = Area per person.
    Final Answer:-
    ∴ Area per person for the given state is 87,310.

    A state has an area of approximately 9,604,100,000 square miles and has approximately 110,000 people. How much area is this per person?

    Maths-General
    Hint:-
    1. In Mathematics, lets say, "a" represents a number and "n" is the number of times that number is to be multiplied with itself, in order to get a desired result. Then, such result can be written as an, where a is called the base and n is its power/ exponent.
    an = a × a × ... × a             n times.
    2. Total Area = Number of people living in the area × Area per person.
    Step-by-step solution:-
    Total Area = 9604100000 sq. miles …................................................ (Equation i)
    Number of people living in the area = 110000 …............................. (Equation ii)
    Now, we know that-
    Total Area = Number of people living in the area × Area per person
    ∴ 9604100000 = 110000 × Area per person
    ∴ 9604100000 / 110000 = Area per person
    ∴ 87,310 = Area per person.
    Final Answer:-
    ∴ Area per person for the given state is 87,310.
    General
    Maths-

    Convert the following fractions to repeating decimals
    d) 1 over 6

    Complete step by step solution:
    (d) On dividing 1 by 6, we have 0.1666666666.. as the corresponding decimal number.

    Convert the following fractions to repeating decimals
    d) 1 over 6

    Maths-General
    Complete step by step solution:
    (d) On dividing 1 by 6, we have 0.1666666666.. as the corresponding decimal number.
    parallel
    General
    Maths-

    Convert the following fractions to repeating decimals
    c) 10 over 33

    Complete step by step solution:
    (c) On dividing 10 by 33, we have 0.3030303030.. as the corresponding decimal number.

    Convert the following fractions to repeating decimals
    c) 10 over 33

    Maths-General
    Complete step by step solution:
    (c) On dividing 10 by 33, we have 0.3030303030.. as the corresponding decimal number.
    General
    Maths-

    Convert the following fractions to repeating decimals
    b) 7 over 18

    Complete step by step solution:
    (b) On dividing 7 by 18, we have 0.3888888888.. as the corresponding decimal number.

    Convert the following fractions to repeating decimals
    b) 7 over 18

    Maths-General
    Complete step by step solution:
    (b) On dividing 7 by 18, we have 0.3888888888.. as the corresponding decimal number.
    General
    Maths-

    Convert the following fractions to repeating decimals
    a) 11 over 12

    Complete step by step solution:
    (a) On dividing 11 by 12, we have 0.9166666666.. as the corresponding decimal number.

    Convert the following fractions to repeating decimals
    a) 11 over 12

    Maths-General
    Complete step by step solution:
    (a) On dividing 11 by 12, we have 0.9166666666.. as the corresponding decimal number.
    parallel
    General
    Maths-

    Convert the following repeating decimals to fractions
    d) 3.25252525252...............

    Complete step by step solution:
    (d) Let x = 0.25252525
    Now multiply by 100 on both the sides,
    We get, 100x = 25.252525
    On subtracting x from both the sides, we have
    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 100 x minus x equals 25.252525 minus 0.25252525 end cell row cell not stretchy rightwards double arrow 99 x equals 25 end cell row cell not stretchy rightwards double arrow x equals 25 over 99 end cell end table
    Now we have a fraction for 0.252525. On adding it with 3, we have
    rightwards double arrow 3 space plus space 25 over 99
    rightwards double arrow 322 over 99 as fraction
    Hence 3.25252525….= 322 over 99

    Convert the following repeating decimals to fractions
    d) 3.25252525252...............

    Maths-General
    Complete step by step solution:
    (d) Let x = 0.25252525
    Now multiply by 100 on both the sides,
    We get, 100x = 25.252525
    On subtracting x from both the sides, we have
    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 100 x minus x equals 25.252525 minus 0.25252525 end cell row cell not stretchy rightwards double arrow 99 x equals 25 end cell row cell not stretchy rightwards double arrow x equals 25 over 99 end cell end table
    Now we have a fraction for 0.252525. On adding it with 3, we have
    rightwards double arrow 3 space plus space 25 over 99
    rightwards double arrow 322 over 99 as fraction
    Hence 3.25252525….= 322 over 99
    General
    Maths-

    Convert the following repeating decimals to fractions
    c) 0.2151515151515........

    Complete step by step solution:
    (c) Let x = 0.215151515…(i)
    Now multiply by 10 on both the sides in (i),
    We get, 10x = 2.151515
    Now multiply by 100 on both the sides in (i),
    100x = 21.51515
    Now multiply by 1000 on both the sides in (i),
    1000x = 215.151515
    On subtracting 10x from both the sides, we have
    1000 x minus 10 x equals 215.1515 minus 2.151515
    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 990 x equals 213 end cell row cell not stretchy rightwards double arrow x equals 213 over 990 end cell end table
    On simplification, we have x equals 71 over 330
    Hence 0.2151515151515....... = 71 over 330

    Convert the following repeating decimals to fractions
    c) 0.2151515151515........

    Maths-General
    Complete step by step solution:
    (c) Let x = 0.215151515…(i)
    Now multiply by 10 on both the sides in (i),
    We get, 10x = 2.151515
    Now multiply by 100 on both the sides in (i),
    100x = 21.51515
    Now multiply by 1000 on both the sides in (i),
    1000x = 215.151515
    On subtracting 10x from both the sides, we have
    1000 x minus 10 x equals 215.1515 minus 2.151515
    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 990 x equals 213 end cell row cell not stretchy rightwards double arrow x equals 213 over 990 end cell end table
    On simplification, we have x equals 71 over 330
    Hence 0.2151515151515....... = 71 over 330
    General
    Maths-

    Convert the following repeating decimals to fractions
    b) 1.5555555555555

    Complete step by step solution:
    (b) Let x = 0.55555555
    Now multiply by 10 on both the sides,
    We get, 10x = 5.5555555
    On subtracting x from both the sides, we have
    table attributes columnspacing 1em end attributes row cell 10 x minus x equals 5.55555555 minus 0.555555555 end cell row cell not stretchy rightwards double arrow 9 x equals 5 end cell row cell not stretchy rightwards double arrow x equals 5 over 9 end cell end table
    Now we have a fraction for 0.5555555. On adding it with 1, we have
    not stretchy rightwards double arrow 1 plus 5 over 9
    not stretchy rightwards double arrow 14 over 9as fraction

    Convert the following repeating decimals to fractions
    b) 1.5555555555555

    Maths-General
    Complete step by step solution:
    (b) Let x = 0.55555555
    Now multiply by 10 on both the sides,
    We get, 10x = 5.5555555
    On subtracting x from both the sides, we have
    table attributes columnspacing 1em end attributes row cell 10 x minus x equals 5.55555555 minus 0.555555555 end cell row cell not stretchy rightwards double arrow 9 x equals 5 end cell row cell not stretchy rightwards double arrow x equals 5 over 9 end cell end table
    Now we have a fraction for 0.5555555. On adding it with 1, we have
    not stretchy rightwards double arrow 1 plus 5 over 9
    not stretchy rightwards double arrow 14 over 9as fraction
    parallel
    General
    Maths-

    Convert the following repeating decimals to fractions
    a) 1.233333333333333333

    Complete step by step solution:
    (a) Let x = 0.23333333…(i)
    Now multiply by 10 on both the sides in (i),
    We get, 10x = 2.3333333
    Now multiply by 100 on both the sides in (i),
    100x = 23.3333333
    On subtracting 10x from both the sides, we have
    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 100 x minus 10 x equals 23.3333 minus 2.3333333 end cell row cell not stretchy rightwards double arrow 90 x equals 21 end cell row cell not stretchy rightwards double arrow x equals 21 over 90 end cell end table
    On simplification, we get x equals 7 over 30
    Now we have a fraction for 0.2333333…. On adding it with 1, we have
    not stretchy rightwards double arrow 1 plus 7 over 30
    not stretchy rightwards double arrow 37 over 30 as fraction

    Convert the following repeating decimals to fractions
    a) 1.233333333333333333

    Maths-General
    Complete step by step solution:
    (a) Let x = 0.23333333…(i)
    Now multiply by 10 on both the sides in (i),
    We get, 10x = 2.3333333
    Now multiply by 100 on both the sides in (i),
    100x = 23.3333333
    On subtracting 10x from both the sides, we have
    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 100 x minus 10 x equals 23.3333 minus 2.3333333 end cell row cell not stretchy rightwards double arrow 90 x equals 21 end cell row cell not stretchy rightwards double arrow x equals 21 over 90 end cell end table
    On simplification, we get x equals 7 over 30
    Now we have a fraction for 0.2333333…. On adding it with 1, we have
    not stretchy rightwards double arrow 1 plus 7 over 30
    not stretchy rightwards double arrow 37 over 30 as fraction
    General
    Maths-

    Convert the following repeating decimals to fractions
    d) 0.488888888888

    Complete step by step solution:
    (d) Let x = 0.4888888888
    Now multiply by 10 on both the sides,
    We get, 10x = 4.888888888
    On subtracting  from both the sides, we have
    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 10 x minus x equals 4.88888888 minus 0.48888888 end cell row cell not stretchy rightwards double arrow 9 x equals 4.4 end cell row cell not stretchy rightwards double arrow x equals fraction numerator 4.4 over denominator 9 end fraction end cell end table
    Multiply by 10 on numerator and denominator of x.
    On multiplying, we have 22 over 45. (Since the numerator and denominator of a fraction must be integers)
    On simplification, we get 22 over 45
    Hence 0.4888888 …. = 22 over 45
     

    Convert the following repeating decimals to fractions
    d) 0.488888888888

    Maths-General
    Complete step by step solution:
    (d) Let x = 0.4888888888
    Now multiply by 10 on both the sides,
    We get, 10x = 4.888888888
    On subtracting  from both the sides, we have
    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 10 x minus x equals 4.88888888 minus 0.48888888 end cell row cell not stretchy rightwards double arrow 9 x equals 4.4 end cell row cell not stretchy rightwards double arrow x equals fraction numerator 4.4 over denominator 9 end fraction end cell end table
    Multiply by 10 on numerator and denominator of x.
    On multiplying, we have 22 over 45. (Since the numerator and denominator of a fraction must be integers)
    On simplification, we get 22 over 45
    Hence 0.4888888 …. = 22 over 45
     
    General
    Maths-

    Convert the following repeating decimals to fractions
    c) 0.366666666666

    Complete step by step solution:
    (c) Let x = 0.3666666
    Now multiply by 10 on both the sides,
    We get, 10x = 3.666666
    On subtracting x from both the sides, we have
    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 10 x minus x equals 3.666666 minus 0.3666666 end cell row cell not stretchy rightwards double arrow 9 x equals 3.3 end cell row cell not stretchy rightwards double arrow x equals fraction numerator 3.3 over denominator 9 end fraction end cell end table
    Multiply by 10 on numerator and denominator of x.
    On multiplying, we have .11 over 30 (Since the numerator and denominator of a fraction must be integers)
    On simplification, we get 11 over 30
    Hence 0.3666666…. = 11 over 30
     

    Convert the following repeating decimals to fractions
    c) 0.366666666666

    Maths-General
    Complete step by step solution:
    (c) Let x = 0.3666666
    Now multiply by 10 on both the sides,
    We get, 10x = 3.666666
    On subtracting x from both the sides, we have
    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 10 x minus x equals 3.666666 minus 0.3666666 end cell row cell not stretchy rightwards double arrow 9 x equals 3.3 end cell row cell not stretchy rightwards double arrow x equals fraction numerator 3.3 over denominator 9 end fraction end cell end table
    Multiply by 10 on numerator and denominator of x.
    On multiplying, we have .11 over 30 (Since the numerator and denominator of a fraction must be integers)
    On simplification, we get 11 over 30
    Hence 0.3666666…. = 11 over 30
     
    parallel

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