# APPROXIMATION

Welcome to class!

In today’s class, we will be talking about approximation. Enjoy the class!

### APPROXIMATION

It is the degree of accuracy of numbers and how to determine it. Rounding up of numbers, significant figures, decimal places, nearest whole numbers, tens, hundreds, and thousand, rounding up of numbers to nearest tenths, hundredths and thousandths

What is approximation?

An approximation is anything similar, but not exactly equal, to something else. A number can be approximated by rounding. A calculation can be approximated by rounding the values within it before performing the operations.

• #### Rounding Numbers to the nearest 10, 100, 1,000:

To approximate to the nearest ten, look at the digit in the ten’s column.

To approximate to the nearest hundred, look at the digit in the hundred’s column.

For the nearest thousand, look at the digit in the thousand’s column.

Then do the following:

1. draw a vertical line to the right of the place value digit that is required
2. look at the next digit
3. if it’s 5 or more, increase the previous digit by one
4. if it’s 4 or less, keep the previous digit the same
5. fill any spaces to the right of the line with zeros.

Examples:

Round 4,853 to the nearest 10, 100 and 1,000.

• 485|3to the nearest 10 is 4,850
• 48|53 to the nearest 100 is 4,900
• 4|853 to the nearest 1,000 is 5,000

Round 76,982 to the nearest 10, 100 and 1,000.

• 7698|2to the nearest 10 is 76,980
• 769|82 to the nearest 100 is 77,000
• 76|982 to the nearest 1,000 is 77,000

Notice that in some cases the answers for rounding are the same.

• #### Rounding to decimal places:

When rounding using decimal places(d.p), the degree of accuracy that is required is usually given. However, there are certain calculations where the degree of accuracy may be more obvious. For example, calculations involving money should be given to two decimal places to represent the pence.

To round to a decimal place:

1. look at the first digit after the decimal point if rounding to one decimal place or the second digit for two decimal places
2. draw a vertical line to the right of the place value digit that is required
3. look at the next digit
4. if the next digit is 5 or more, increase the previous digit by one
5. if it’s 4 or less, keep the previous digit the same
6. remove any numbers to the right of the line

Examples:

Round 248.561 to 1 decimal place, then round it to 2 decimal places:

• 5|61 to 1 decimal place is 248.6
• 56|1to 2 decimal place is 248.56

Notice that your answer should have the same number of decimal places as the approximation asked for.

Round 0.08513 to 1 decimal place and then to 2 decimal places:

• 0|8513 to 1 decimal place is 0.1
• 08|513 to 2 decimal places is 0.09

• #### Rounding to significant figures:

The method of rounding to a significant figure is often used as it can be applied to any kind of number, regardless of how big or small it is. When a newspaper reports a lottery winner has won £3 million, this has been rounded to one significant figure. It rounds to the most important figure in the number.

To round to a significant figure:

1. look at the first non-zero digit if rounding to one significant figure
2. look at the digit after the first non-zero digit if rounding to two significant figures
3. draw a vertical line after the place value digit that is required
4. look at the next digit
5. if the next digit is 5 or more, increase the previous digit by one
6. if it is 4 or less, keep the previous digit the same
7. fill any spaces to the right of the line with zeros, stopping at the decimal point if there is one

Example:

Round 53,879 to 1 significant figure, then 2 significant figures.

• 5|3879 to 1 significant figure is 50,000
• 53|879 to 2 significant figures is 54,000

Notice that the number of significant figures in the question is the maximum number of non-zero digits in your answer.

Round 0.005089 to 1 significant figure, then 2 significant figures.

• 005|089 to 1 significant figure is 0.005
• 0050|89 to 2 significant figures is 0.0051

Question

What is 98,347 rounded to 1 significant figure, and 2 significant figures?

In our next class, we will be talking more about Approximation.  We hope you enjoyed the class.

Should you have any further question, feel free to ask in the comment section below and trust us to respond as soon as possible.

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