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# Significant Digits

Significant digits, also known as significant figures, measure the overall relative accuracy of a value. They represent the number of digits that are considered meaningful in a measurement.

## The rules of significant digits

Significant digits can be a bit confusing if you're not sure which are deemed significant and which are not. Here's a look at some rules for identifying significant digits in a number:

1. All non-zero digits are significant (ex.: In 546, there are 3 significant digits).
2. All zeros in between two non-zero digits are significant (ex.: In 7906, there are 4 significant digits).
3. Zeros that trail non-zero digits with a decimal are significant (ex.: In 780.0, there are 4 significant digits).
4. Zeros in a whole number that trail non-zero digits with no decimal point are not significant (ex.: In 780, there are only 2 significant digits). Though, an exception can be made to keep the zeros if they are needed for a specific measurement.
5. Leading zeros (zeros in front of non-zero digits) are not significant (ex.: In 0.0023935, there are five significant digits).

## Identifying significant digits examples

Let's look at numbers with similar digits that have a different number of significant digits:

0.054 has 2 significant digits

0.504 has 3 significant digits

504.0 has 4 significant digits

504.00 has 5 significant digits

5004.00 has 6 significant digits

0.000834 has 3 significant digits

0.008034 has 4 significant digits

0.080034 has 5 significant digits

0.803400 has 6 significant digits

8.003400 has 7 significant digits

## Rounding significant digits

Rounding is a way to eliminate some digits you don't need in a number while maintaining a level of accuracy. The person rounding a number typically decides how many significant digits they'd like to keep based on their measurement requirements. Before looking at how to round significant digits, let's look at some important terms related to rounding:

• The most significant digit is the leftmost significant digit in a number (ex. In 7.56109, the 7 is the most significant digit).
• While the least significant digit is typically the rightmost significant digit, for the purposes of rounding, it is the last significant digit that you want to keep (ex. If you want to keep 3 significant digits in 7.56109, the least significant digit is 6)
• The first non-significant digit is the first digit to the right of the least significant digit (ex. If you want to keep 3 significant digits in 7.56109, the first non-significant digit is 1).

## The rules of rounding

• The least significant digit doesn't change if the first non-significant digit is less than five. For example, if you want to round 342.123 to 4 significant digits, you'll drop the last two digits and keep 342.1.
• If the first non-significant digit is 5 or greater, the least significant digit goes up by 1 digit. So, if you want to round 57.1236 to 5 significant digits, you'll drop the 6, change 3 to 4, and you're left with 57.124.
• If you're rounding an integer, you'll replace digits following the least significant digit. So, if you want to round 6761 to two significant digits, you'll replace 6 and 1 with two zeros as placeholders and round up (since the first non-significant digit is 6) so that the number reads 6800.

## Practice questions on significant digits

a. How many significant digits are in the number 0.172693?

b. How many significant digits are in the number 89.300?

c. How many significant digits are in the number 0.000235?

d. How many significant digits are in the number 745300?

Answer: 4 (unless one or both of the zeros are needed for the measurement)

e. What is 12.7803 when rounded to 3 significant digits?

f. What is 6392.81 when rounded to 5 significant digits?

g. What is 1.338 when rounded to 2 significant digits?

h. What is 788.66 when rounded to 4 significant digits?