### Key Concepts

- Introduction to Comparing Numbers
- Compare Whole Numbers
- Round Whole Numbers

**Comparing Numbers: Compare Whole Numbers **

Comparing is the process in which we observe similar properties of different objects or things,

for example, we compare common features and prices before buying mobile phones.

Similarly, in math, we compare the place values to find greater or smaller numbers.

Place Value | 1^{st} Number Face Values | <, >, = | 2^{nd} Number Face Values |

Thousands | 5 | > | 3 |

Hence, 5214 is greater than 3122.

**Step 3:** If the higher place values have the same face values, then compare the lower face values.

Place Value | 1^{st} Number Face Values | <, >, = | 2^{nd} Number Face Values |

Thkousands | 3 | = | 3 |

Hundreds | 2 | = | 2 |

Tens | 4 | < | 6 |

Hence, 3242 is less than 3263.

**Round Whole Numbers**

#### Rounding Off Numbers

‘Rounding’ means the process of making a number simpler such that its value remains close to what it was. The result obtained after rounding off a number is less accurate but easier to use.

**Rules for Rounding Numbers:**

There are a certain set of rules that need to be followed to round off a number. The following table shows these rules for different cases:

SI. No. | Rules |

1 | All the non-zero digits in the number are significant. |

2 | All the zeroes that are between non-zero digits are significant. |

3 | The zeroes on the right of a non-zero digit in a whole number are significant. |

4 | If the digit to be dropped while rounding off is less than 5, the following digit is left unchanged. |

5 | If the digit to be dropped while rounding off is 5 or greater than 5, the following digit is increased by 1. |

6 | While rounding off a digit at a higher place value, we ignore the lower place value digits. |

**Types of Rounding of Whole Numbers **

**Rounding off a number to nearest tens:**

While comparing digits, we observe that the numbers 1, 2, 3, and 4 are nearer to 0. So, these numbers are rounded off to their lower tens value. Similarly, numbers 6, 7, 8, and 9 are nearer to 10. So, these numbers are rounded off to their higher tens value.

What about number 5?

Since number 5 is equidistant from both 0 and 10 thus, it is rounded off to the higher ten.

**Rounding off a number to nearest hundreds:**

Suppose we have numbers from 801 to 849. All the numbers are closer to 800 in comparison to 900. So, these numbers will be rounded off to their nearest hundreds, i.e., 800. Similarly, numbers 851 to 899 are closer to 900. So, these numbers will be rounded off to the higher hundreds, that is, 900.

**Rounding off a number to nearest thousands:**

**Exercise:**

- Round 801,821 to the nearest ten thousand.
- Jamie’s class sold 1,862 tickets for the school raffle and Eric’s class sold 2,139 tickets.

Whose class sold more tickets? - Nina is in Eric’s class. She climbed up to 8,789 feet on Telescope Peak. Telescope Peak is 11,049 feet tall at its highest point. Write an expression using < or > to show the heights Nina, Jamie, and Eric climbed from the least to the greatest.
- Write these numbers in order from the least to the greatest:

3.24, 4.02, 3.44 - Jake has $34.82, Emily has $38.42, and Will has $34.28. Who has the most money? Who has the least?
- Jessica is comparing the numbers 5,553,402 and 5,554,937. She thinks she can tell which one is greater by looking in the hundred thousands place. Is she correct? Explain.
- Maxine and Sam biked for six hours a day for five days. When they stopped, Sam had gone 2,376,827 feet and Maxine had gone 2,376,791 feet. Who went farther?
- Write 62,403,000 in expanded notation.
- The Marris family’s warehouse contains 10 apples, 7,000 bananas, 20,000 plums, 300 oranges, and 100,000 grapes. Write the total number of pieces of fruit in standard form.
- The tallest mountain in California is Mt. Whitney. It is 14,491 feet tall. Round its height to the nearest thousand.