**Evaluating Exponents for Decimals** *KS3 Revision*

## What you need to know

**Things to remember:**

- Multiplying the original number of decimal places by the power tells you how many decimals you will have.
- Evaluating the exponent without the decimal will help you check if the numbers in your answer are in the correct order.

An exponent is a number written to the top right of a number and tells us how many times we multiply a number by itself.

6^2 = 6\times 6

6^3 = 6\times 6\times 6

6^4= 6\times 6\times 6\times 6

So, all we’re doing when we have exponents is lots of multiplications. When we do these multiplications, we refer to it as “evaluating the exponent”.

*Evaluate the following exponents:*

* *

5^2=5\times5=25

7^3=7\times7\times7=343

8^4=8\times8\times8\times8=4096

Evaluating decimal numbers is a little trickier, but we have some steps that can help us.

*Evaluate 0.08^3*

** **

**Step 1: **Count the number of decimal places.

There are two decimal places.

** **

**Step 2:** Multiply the number in **Step 1** by the power in the question.

2\times3=6

This number gives how many decimal places there will be in the final answer.

** **

**Step 3: **Ignore the decimal point in the original question and evaluate.

8^3=512

** **

**Step 4: **Set up a number filled with 0s and as many decimal places as there were in **Step 2**.

0.000000

**Step 5: **Put the number in **Step 3** into the decimal in **Step 4**, starting from the right.

0.000002

0.000012

0.000512

0.08^3=0.000512

*Evaluate 2.3^4*

** **

**Step 1: **Count the number of decimal places.

There’s one decimal places.

** **

**Step 2:** Multiply the number in **Step 1** by the power in the question.

1\times4=4

** **

**Step 3: **Ignore the decimal point in the original question and evaluate.

23^4=279841

** **

**Step 4: **Set up a number filled with 0s and as many decimal places as there were in **Step 2**.

0.0000

**Step 5: **Put the number in **Step 3** into the decimal in **Step 4**, starting from the right.

0.0001

0.0041

0.0841

0.9841

7.9841

** **

Although we have run out of 0s to replace, we can put the last number onto the left.

27.9841

## Example Questions

**Question 1:** Evaluate 1.7^3.

**Step 1: **Count the number of decimal places.

There’s one decimal places.

** **

**Step 2:** Multiply the number in **Step 1** by the power in the question.

1\times3=3

**Step 3: **Ignore the decimal point in the original question and evaluate.

17^3=4913

** **

**Step 4: **Set up a number filled with 0s and as many decimal places as there were in **Step 2**.

0.000

**Step 5: **Put the number in **Step 3** into the decimal in **Step 4**, starting from the right.

0.003

0.013

0.913

4.913

**Question 2:** Evaluate 0.02^5

**Step 1: **Count the number of decimal places.

There are two decimal places.

** **

**Step 2:** Multiply the number in **Step 1** by the power in the question.

2\times5=10

**Step 3: **Ignore the decimal point in the original question and evaluate.

2^5=32

** **

**Step 4: **Set up a number filled with 0s and as many decimal places as there were in **Step 2**.

0.0000000000

**Step 5: **Put the number in **Step 3** into the decimal in **Step 4**, starting from the right.

0.0000000002

0.0000000032