11+ Maths Solved Topic Wise Questions

1. What is Rounding of Numbers?

Rounding off makes the number simple by keeping its value intact but closer to the next number. Many physical quantities like the amount of money, distance covered, length measured, etc are estimated by rounding off the actual number to the nearest possible whole number.

For example:

1. £29.99 could be rounded to £30.
2. 57 minutes could be rounded to an hour.

1.1 Rounding of Whole and Decimal Numbers

We follow the below steps while rounding whole numbers and decimals:

• Observe the next smaller place value i.e towards the right of the digit that is being rounded off. For example, for rounding to the nearest hundred, observe the digit in the tens place.
• If the digit in the smaller place value is less than 5, then we round down. To round down, replace all the digits after the digit that you are rounding to by 0.

• If the digit in the smaller place value is greater than or equal to 5, then we round up. To round up, add one to the digit that you are rounding to and replace all the digits after it with 0.

1.2 Rounding Off - Example

Example:

Round the following numbers to nearest ten:

1. 413.5
2. 399

Solution:

• Identify the digit in the tens place: 1

  Look at the digit to the right  of the digit to be rounded: 3

  Work out whether to round up or round down: If the digit to the right is greater than or equal to 5, then round up the digit. Otherwise, round down the digit.

  Here, 3 < 5 i.e. round down. So, the digit to be rounded (1) remains unchanged.

  Every other digit after it becomes zero.

  Answer is 410

• Identify the digit in the tens place: 9

  Look at the digit to the right  of the digit to be rounded: 9

  Work out whether to round up or round down: If the digit to the right is greater than or equal to 5, then round up the digit. Otherwise, round down the digit.

  Here, 9 > 5 i.e. round up. So, 9 + 1 = 10, and this 1 is carried over to the hundreds place to give 3 + 1 = 4

  Every other digit after it becomes zero.

  Answer is 400

Example:

Round 9460 to the nearest thousand.

Solution:

Consider thousands place and follow the steps as given below:

Work out which digit  you need to round: 9

Look at the digit to the right  of the digit to be rounded: 4

Work out whether to round up or round down: If the digit to the right is greater than or equal to 5, then round up the digit. Otherwise, round down the digit.

Every other digit after it becomes zero.

Answer is 9000

Example:

Round 0.93 to the nearest tenth.

Solution:

Work out which digit  you need to round: 9

Look at the digit to the right  of the digit to be rounded: 3

Work out whether to round up or round down: If the digit to the right is greater than or equal to 5, then round up the digit. Otherwise, round down the digit.

Here, 3 < 5 i.e. round down. So, the digit to be rounded (9) remains unchanged.

Every other digit after it becomes zero.

Answer is 0.9