Step by step
The question
Question: estimate 41.3 × 9.79 ÷ 0.765.
To estimate means to find about how big the answer is.
We make every number easy first.
1 Round to 1 significant figure
We round each number to 1 significant figure: only its first figure stays.
41.3: the first figure is 4.
The next digit is 1, 4 or less, so we round down: 40.
9.79: the first figure is 9.
The next digit is 7, 5 or more, so we round up: 10.
0.765: the first figure is 7.
The next digit is 6, 5 or more, so we round up: 0.8.
2 Work it out
So the answer is about 40 × 10 ÷ 0.8.
Now it is easy to work out.
Careful!
We changed the numbers.
So we write ≈, about, not =.
40 times 10 is 400.
400 divided by 0.8 is 500.
To divide by 0.8, we move the point in both numbers 1 place: 4000 divided by 8.
That is 500.
So the answer is about 500.
3 Check
Let's check with a calculator.
The exact answer is about 528.5.
That is close to 500.
So the estimate is good!
Let's look back.
First: round to 1 significant figure.
Then: work it out.
Last: check.