Significant figures facts for kids

Significant figures are the important digits in a number or a measurement. They tell us how precise or exact a number is. Think of it like this: if you measure something with a ruler that only has centimeter marks, your measurement won't be as exact as if you use a ruler with millimeter marks. Significant figures help us show that level of exactness.

For example, if you see the number 2300, it might have two significant figures (the 2 and the 3). This means the measurement was probably rounded to the nearest hundred. But if you see 2040, it has three significant figures (2, 0, and 4), showing it's a bit more precise.

What Are Significant Figures?

Significant figures (often called "sig figs") are the digits in a number that carry meaning about its precision. When you measure something, you can only be so accurate. Significant figures help us show how reliable our measurement or calculation is. They tell us which digits are known for sure and which ones are just placeholders.

Why Are They Important?

Imagine you're baking a cake. If a recipe says "add 2 cups of flour," you might use a measuring cup that's marked for cups. You wouldn't use a super precise scale that measures down to tiny grams, because the recipe doesn't need that much detail. Significant figures work similarly in science and math. They make sure we don't pretend our numbers are more accurate than they actually are.

• They show the precision of a measurement.
• They help avoid giving a false sense of accuracy in calculations.
• They are used a lot in science, engineering, and chemistry.

Rules for Counting Significant Figures

It's important to know how to count significant figures correctly. Here are the main rules:

Non-Zero Digits

Any digit that is not zero is always significant.

• Example: The number 456 has three significant figures (4, 5, and 6).
• Example: The number 1.234 has four significant figures (1, 2, 3, and 4).

Zeros Between Non-Zero Digits

Zeros that are "sandwiched" between non-zero digits are always significant.

• Example: The number 205 has three significant figures (2, 0, and 5).
• Example: The number 10.08 has four significant figures (1, 0, 0, and 8).

Leading Zeros

Zeros that come before non-zero digits (leading zeros) are never significant. They are just placeholders to show where the decimal point is.

• Example: The number 0.007 has one significant figure (7). The zeros just show it's a very small number.
• Example: The number 0.025 has two significant figures (2 and 5).

Trailing Zeros (at the End of a Number)

This is where it gets a bit tricky, depending on whether there's a decimal point.

Trailing Zeros with a Decimal Point

If a number has a decimal point, any zeros at the very end (trailing zeros) are significant. This shows that these zeros were actually measured or are important for precision.

• Example: The number 5.00 has three significant figures (5, 0, and 0). This means it's precisely 5.00, not just "about 5".
• Example: The number 120.0 has four significant figures (1, 2, 0, and 0).

Trailing Zeros Without a Decimal Point

If a number does not have a decimal point, trailing zeros are usually not considered significant. They are often just placeholders.

• Example: The number 2300 has two significant figures (2 and 3). The zeros are just showing it's in the thousands.
• Example: The number 5000 has one significant figure (5).

Important Note: Sometimes, if a trailing zero in a whole number was actually measured, it can be made significant by adding a decimal point. For example, 2300. would have four significant figures.

Significant Figures in Calculations

When you add, subtract, multiply, or divide numbers, the answer should not be more precise than the least precise number you started with. Significant figures help us round our answers correctly.

Addition and Subtraction

When you add or subtract numbers, your answer should have the same number of decimal places as the number with the fewest decimal places.

• Rule: Look at the decimal places, not the total significant figures.
• Example:

* 2.345 (3 decimal places) * + 1.2 (1 decimal place) * = 3.545 * Since 1.2 has only one decimal place, your answer should be rounded to one decimal place: 3.5

Multiplication and Division

When you multiply or divide numbers, your answer should have the same number of significant figures as the number with the fewest significant figures.

• Rule: Look at the total significant figures.
• Example:

* 2.5 (2 significant figures) * x 3.45 (3 significant figures) * = 8.625 * Since 2.5 has the fewest significant figures (two), your answer should be rounded to two significant figures: 8.6

Rounding Rules

After a calculation, you often need to round your answer to the correct number of significant figures or decimal places.

• If the first digit to be dropped is 5 or greater, round up the last kept digit.
• If the first digit to be dropped is less than 5, keep the last kept digit the same.

Example: Round 8.625 to two significant figures.

• The first digit to be dropped is 2 (which is less than 5).
• So, the number rounds to 8.6.

Example: Round 8.675 to two significant figures.

• The first digit to be dropped is 7 (which is 5 or greater).
• So, the number rounds up to 8.7.

See also

In Spanish: Cifras significativas para niños