GCSE Rounding Numbers, Estimation, Significant Figures, Decimal Places Questions and Answers

1. Significant Figures

Significant figures are also known as significant digits because they are established in the form of digits. Counting each value starting with the first non-zero digit on the left will reveal the number of meaningful digits. These figures are accurate and essential for indicating how much of a length, volume, mass, measurement, etc. there is.

1.1 Definition

The crucial or important digits that accurately represent the meaning of a certain number are known as the significant figures of that number. 

1.258, for instance, has four significant digits. These substantial figures provide the numbers accuracy. Additionally, they are known as significant digits.

1.2 Rules for Significant Figures

• All non-zero digits are significant. 238745 contains six significant digits.
• All zeros that occur between any two non zero digits are significant. For example, 107.0098 contains seven significant digits.
• All zeros that are on the right of a decimal point and also to the left of a non-zero digit is never significant. For example, 0.00128 contained three significant digits.
• All zeros that are on the right of a decimal point are significant, only if, a non-zero digit does not follow them. For example, 30.00 contains four significant digits.
• All the zeros that are on the right of the last non-zero digit, after the decimal point, are significant. For example, 0.0085200 contains five significant digits.
• All the zeros that are on the right of the last non-zero digit are significant if they come from a measurement. For example, 1040 m contains four significant digits.

1.3 Rounding to significant figures

In order to round to a given number of significant digits, we follow these steps:

1. Locate the significant figure for the degree of accuracy required. The first non-zero digit is the first significant figure.
2. Observe the next digit to the right. Is it 5 or more?
3. If it is 5 or more - round up by adding 1 to the previous digit. If it is less than 5 - round down by keeping the previous digit the same. 
4. If the degree of accuracy is 10 or more, fill in zeros to make the number the correct size.

Example: Write 72.347162 correct to 4 significant digits. 

Solution: The number 72.347162, rounded to 4 significant digits is 72.35

Example: Write 3758 correct to the nearest 1000.

Solution: 3758 correct to the nearest 1000 is 4000.

Example: Write 56.78 correct to one e significant figure.

Solution: 56.78 correct to one significant figure is 60.

1. Decimal Places 

Positions of the digits to the right of a decimal point are known as decimal places. 

A decimal number is shortened to a specific level of accuracy when it is rounded to decimal places. To achieve this, we locate the decimal place to which we want to round the number, and then we look at the digit immediately to its right. We round up if the number following the selected accuracy is a 5 or above. When it falls below 5, we round down.

It is important to give the number of digits required after the decimal point, even if the last digit would be a zero.

Example: Rounding 57.6274 to 2 decimal places (2.d.p) is 57.63

1.1 How to round to Decimal Places?

We follow the below steps while rounding decimals:

1. 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.
2. 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. 
3. 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.

Example: Round 96.237 to the nearest tenth.

Solution:

Example: Round 0.041682 to two decimal places.

Solution: 

Example: A calculator displayed an answer to a calculation as 163.2085313. What is this given to three decimal places?

Solution: