PAIBOTLearn
Sign inSign up

Scientific notation and significant figures

Powers & exponents

Japanese school year: Junior high 1

What you learn

Learn how to express large numbers using powers of ten and handle significant figures, which represent meaningful digits in measurements. This approach is useful for reporting observational data and experimental measurements accurately. Prior knowledge of decimal place value and basic powers will support your understanding.

Go to practice

Key points

This is scientific notation, used to represent very large or tiny numbers clearly. A number is written as the product of aa (1≤a<101 \le a < 10) and an integer power of ten 10n10^n.

a×10n(1≤a<10,  n∈Z)a \times 10^n \quad (1 \le a < 10,\; n \in \mathbb{Z})

This formula defines negative integer powers of 10 as fractions with 10n10^n in the denominator. It writes small decimals neatly, such as 10−1=0.110^{-1} = 0.1 and 10−2=0.0110^{-2} = 0.01.

10−n=110n10^{-n} = \frac{1}{10^n}

This identity defines 10 raised to the power of 0 as 1. It allows single-digit values to be formatted consistently in scientific notation, such as 5=5×1005 = 5 \times 10^0.

100=110^0 = 1

"Significant figures" refer to the meaningful digits in a measured value. Leading zeros used only for placeholding do not count (0.025 has 2 digits), but trailing zeros showing precision (like the 0 in 3.20) do count.

Choose a set to practice.