How many significant figures in 7.00 × 10^3?

Three significant figures.

Seven point zero zero times ten to the three means there are three significant figures because every nonzero digit and every zero between or after a decimal significant digit counts; the digits shown before the times-ten part are seven, zero, zero and all three are significant. Think of the written number as seven point zero zero times ten to the three rather than seven thousand with hidden zeros, because the scientific notation makes clear which digits are measured.

Scientific notation helps show precision: when you write seven point zero zero times ten to the three you are telling someone you measured to the hundreds place and the last two zeros are meaningful, not just placeholders; if you had written seven times ten to the three you would only have one significant figure and that would mean you knew only the thousands place; if you had written seven point zero times ten to the three you would have two significant figures. Remember that zeros after the decimal point and after a nonzero digit are significant, while zeros used only to place the decimal in large numbers without a decimal point are not significant.

A common mistake is treating all zeros as not significant, but trailing zeros after a decimal are significant and show precision, so write numbers in scientific notation when you want to be clear; another error is failing to convert back and forth correctly between plain numbers and scientific notation, so practice rewriting numbers like seven point zero zero times ten to the three as seven thousand to see why the notation matters; finally some students miscount when there is no decimal point in large numbers, so use scientific notation to avoid ambiguity and always count only the digits shown as measured. Visit w w w dot gumball degree dot com to find more videos and resources on significant figures.

Significant Figures in 7.00 × 10^3

1. Use scientific notation to show precision
2. Write 7.00×10^3, not 7000
3. Trailing zeros after decimal are meaningful
4. Seven has three significant digits
5. One-digit 7×10^3 shows less precision

Common Significant Figures Mistakes

1. Treating all zeros as not significant
2. Not using scientific notation for clarity
3. Miscounting digits without a decimal

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