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Method

Rounding to Significant Figures

Rounding a number to n significant figures means to rewrite the number so that it has exactly n significant figures. The result is an approximation of the number.

The number 6213.4983 rounded to three significant figures becomes 6.21* 10^3.

The following steps should be followed to round a number to n significant figures.

Look For the nth Significant Figure

Consider the number 6213.4983. In each column, the corresponding significant figure is highlighted.

Round to Three Significant Figures	Round to Five Significant Figures	Round to Six Significant Figures
62 13.4983	6217. 3983	6217.3 983

Draw a Vertical Bar to the Right of This Digit

Round to Three Significant Figures	Round to Five Significant Figures	Round to Six Significant Figures
62 1\|3.4983	6213. 4\|983	6213.4 9\|83

Look at the Digit to the Right of the Bar

If it is less than 5, keep the nth digit the same.

If it is 5 or more, increase the nth digit by 1.
- If the nth digit becomes 10, write 0 instead and increase the previous digit by 1. Repeat this as many times as needed.

Round to Three Significant Figures	Round to Five Significant Figures	Round to Six Significant Figures
62 1\| 3.4983 ↓ 62 1\| 3.4983	6213. 4\| 983 ↓ 6213. 5\| 983	6213.4 9\| 83 ↓ 6213.410\| 83 ↓ 6213. 5 0\| 83

Look at the Digits to the Right of the nth Significant Figure

Remove the bar.
From the nth digit, any digit to the left of the decimal point must be replaced with zero.
From the nth digit, any digit to the right of the decimal point must be removed.

The following table shows the results of rounding 6203.4983 to 3, 5, and 6 significant figures.

Round to Three Significant Figures	Round to Five Significant Figures	Round to Six Significant Figures
62 1 3.4983 ↓ 6210	6213. 5 983 ↓ 6213.5	6213.5 0 83 ↓ 6213.50

Extra

When The Rounded Number Has Fewer Digits Than the Original

It may happen that rounding a number results in an integer with fewer digits than the number of digits of the integer part of the original number. In this case, a bar is drawn above the last significant digit to indicate that there were more significant digits.

Rounding the Number 43 346 to
Two Significant Figures	Three Significant Figures	Four Significant Figures
43 000 or 4.3* 10^4	43 300 or 4.33* 10^4	43 350 or 4.335* 10^4

Alternatively, writing the number using scientific notation helps identify the number of significant figures.

Exercises

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