Computing with scientific notation

Warm-up

Three quick questions from earlier lessons.

Discover

$(2 \times 10^3)(4 \times 10^5)$ . Group the numbers and the powers of ten. What do you get?

$8 \times 10^8$
$8 \times 10^{15}$

Key idea

Compute with the parts separately.

Multiply or divide: work on the numbers and the powers of 10 separately, then adjust to scientific notation. Add or subtract: rewrite with the same power of 10 first, then add the numbers; the power of 10 stays.

Worked example

$(9 \times 10^7) \div (3 \times 10^2)$ and $5 \times 10^4 + 7 \times 10^4$ .

3 \times 10^5

9 ÷ 3, 7 − 2.

12 \times 10^4 = 1.2 \times 10^5

Like terms.

Your turn, guided

Your turn: $(3 \times 10^2)(2 \times 10^6) = 6 \times 10^{?}$ .

8

2 + 6.

Practice ★

Compute $(3 \times 10^{ 4 }) \cdot (2 \times 10^{ 2 })$ . (An expression with a power of 10 is fine.)
Compute $(3 \times 10^{ 3 }) \cdot (4 \times 10^{ 3 })$ . (An expression with a power of 10 is fine.)

Compute $(4 \times 10^{ 9 }) \div (2 \times 10^{ 4 })$ . (An expression with a power of 10 is fine.)

Watch out!

Practice ★★

Compute $2 \times 10^{ 4 } + 2 \times 10^{ 4 }$ . (An expression with a power of 10 is fine.)
Compute $3 \times 10^{ 4 } + 1 \times 10^{ 4 }$ . (An expression with a power of 10 is fine.)

Boss problem. A phone does about $3 \times 10^9$ operations per second. An old computer did about $1 \times 10^4$ operations per second.

Exit ticket

Three questions to check you have got it.

Compute $(3 \times 10^{ 4 }) \cdot (2 \times 10^{ 2 })$ . (An expression with a power of 10 is fine.)
Compute $(3 \times 10^{ 3 }) \cdot (4 \times 10^{ 3 })$ . (An expression with a power of 10 is fine.)
Compute $(2 \times 10^{ 2 }) \cdot (2 \times 10^{ 3 })$ . (An expression with a power of 10 is fine.)

Summary card

Computing in scientific notation

Multiply/divide: separately. Add/subtract: same power first.

Watch out: adding does not add the exponents.

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