Mathematics • Year 9 • Unit 1 • Lesson 16
Writing Numbers in Scientific Notation
Build fluency CONVERTING any number — big or tiny — into $a \times 10^n$. Slide the decimal to the first non-zero digit, count the places, pick the sign. Watch a worked example, fill in a guided one, then complete eight practice problems.
1. I do — fully worked example
Big number $\Rightarrow$ positive power. Slide the decimal LEFT until it sits just after the first non-zero digit.
Problem. Write $93\,000\,000$ in scientific notation.
Step 1 — Find the decimal point.
$93\,000\,000.$ — the decimal sits at the far right.
Reason: in a whole number, the decimal point is implicit at the end.
Step 2 — Slide the decimal LEFT until just after the first non-zero digit.
$93\,000\,000. \to 9.3\,000\,000$ — moved $7$ places left.
Reason: the new coefficient must satisfy $1 \leq a < 10$, so put the decimal point after the leading "$9$".
Step 3 — The number is BIG, so $n$ is POSITIVE.
$n = +7$ (we shifted $7$ places).
Reason: $93\,000\,000$ is much bigger than $1$, so $10^n$ must make $9.3$ bigger again — positive exponent.
Step 4 — Write as $a \times 10^n$.
$93\,000\,000 = 9.3 \times 10^7$
Reason: drop the trailing zeros from the coefficient; the $10^7$ records them.
Answer: $\mathbf{9.3 \times 10^7}$.
2. We do — fill in the missing steps
Same approach but the working is faded. Fill in each blank. 4 marks
Problem. Write $0.000\,007$ in scientific notation.
Step 1 — Identify the first non-zero digit: it is __________________ .
Step 2 — Slide the decimal RIGHT until it sits just after the first non-zero digit:
$0.000\,007 \to \_\_\_\_\_$ — moved $\_\_\_$ places right.
Step 3 — The number is SMALL (less than $1$), so $n$ is __________________ (positive / negative).
Step 4 — Write as $a \times 10^n$:
$0.000\,007 = \_\_\_\_\_ \times 10^{\_\_\_}$
3. You do — independent practice
Show working under each problem. Foundation = standard big/small. Standard = multiple-digit coefficient. Extension = real measurement and a check.
Foundation — single conversion
3.1 Write $45\,000$ in scientific notation. 1 mark
3.2 Write $5\,200$ in scientific notation. 1 mark
3.3 Write $1\,200\,000$ in scientific notation. 1 mark
3.4 Write $0.000\,082$ in scientific notation. 1 mark
Standard — multi-digit coefficient or large power
3.5 Write $0.000\,486$ in scientific notation. 2 marks
3.6 Write $607\,000\,000$ in scientific notation. 2 marks
Extension — real measurements and a check
3.7 A particular bacterium is $0.000\,002$ m long. Write that length in scientific notation, in metres. 2 marks
3.8 Write the Earth–Sun distance $150\,000\,000\,000$ m in scientific notation. Then CHECK your answer by reading it back as an ordinary number (you should get $150\,000\,000\,000$ again). 3 marks
How did this worksheet feel?
What I'll revisit before next class:
Section 2 — We do (faded $0.000\,007$)
Step 1: first non-zero digit is $\mathbf{7}$.
Step 2: $0.000\,007 \to \mathbf{7}$ — moved $\mathbf{6}$ places right.
Step 3: $n$ is negative (small number).
Step 4: $0.000\,007 = \mathbf{7 \times 10^{-6}}$.
3.1 — $45\,000$
Slide $4$ places left from $45\,000.$ to $4.5$. Big number, positive power: $\mathbf{4.5 \times 10^4}$.
3.2 — $5\,200$
Slide $3$ places left from $5\,200.$ to $5.2$. $\mathbf{5.2 \times 10^3}$.
3.3 — $1\,200\,000$
Slide $6$ places left to $1.2$. $\mathbf{1.2 \times 10^6}$.
3.4 — $0.000\,082$
Slide $5$ places right to $8.2$. Small number, negative power: $\mathbf{8.2 \times 10^{-5}}$.
3.5 — $0.000\,486$
First non-zero digit is $4$. Slide the decimal right past it: $0.000\,486 \to 4.86$ — $4$ places right. Negative power: $\mathbf{4.86 \times 10^{-4}}$.
3.6 — $607\,000\,000$
Slide $8$ places left from $607\,000\,000.$ to $6.07$. Positive power: $\mathbf{6.07 \times 10^8}$.
3.7 — Bacterium length
Slide $6$ places right to $2$. Small number, negative power: $\mathbf{2 \times 10^{-6}}$ m.
3.8 — Earth–Sun distance
$150\,000\,000\,000.$ — slide $11$ places left to $1.5$. Big number, positive power: $\mathbf{1.5 \times 10^{11}}$ m.
Check: $1.5 \times 10^{11}$ means shift the decimal $11$ places right: $1.5 \to 15 \to 150 \to 1\,500 \to \ldots \to 150\,000\,000\,000$ ✓.