Topics › KS3 › Number

Standard form

sf-01 Present from here

Write $34\,000$ in standard form.

Option A: $3.4 \times 10^{3}$

Option B: $34 \times 10^{3}$

Option C: $3.4 \times 10^{5}$

Option D: $3.4 \times 10^{4}$

Answer and misconceptions

Option A: $3.4 \times 10^{3}$ ✗
Uses the number of zeros as the power34 000 has three zeros, but the 3 has moved four places.

Option B: $34 \times 10^{3}$ ✗
Leaves the first number 10 or moreThe first number must be at least 1 and less than 10.

Option C: $3.4 \times 10^{5}$ ✗
Uses the number of digits as the power34 000 has five digits, but 3.4 × 10⁵ = 340 000.

Option D: $3.4 \times 10^{4}$ ✓ Correct
sf-02 Present from here

Write $6.2 \times 10^{-3}$ as an ordinary number.

Option A: $0.00062$

Option B: $0.0062$

Option C: $6200$

Option D: $-0.0062$

Answer and misconceptions

Option A: $0.00062$ ✗
Writes three zeros after the decimal pointUses the index as a count of zeros, not of places moved.

Option B: $0.0062$ ✓ Correct

Option C: $6200$ ✗
Ignores the negative sign in the indexHas multiplied by 1000 instead of dividing by 1000.

Option D: $-0.0062$ ✗
Thinks a negative index makes the number negativeMoves the point correctly but adds a minus sign; a negative index gives a small positive number.
sf-03 Present from here

Which number is written in standard form?

Option A: $70.5 \times 10^{5}$

Option B: $0.705 \times 10^{7}$

Option C: $7.05 \times 10^{6}$

Option D: $7.05 \times 100^{3}$

Answer and misconceptions

Option A: $70.5 \times 10^{5}$ ✗
Allows the first number to be 10 or moreThinks any number × a power of 10 is standard form.

Option B: $0.705 \times 10^{7}$ ✗
Allows the first number to be less than 1The first number must be at least 1.

Option C: $7.05 \times 10^{6}$ ✓ Correct

Option D: $7.05 \times 100^{3}$ ✗
Thinks any power of 10 can be the baseStandard form always uses 10 as the base.
sf-04 Present from here

Which number is the largest?

Option A: $9.9 \times 10^{3}$

Option B: $2.1 \times 10^{4}$

Option C: $1.5 \times 10^{-5}$

Option D: $21\,000 \times 10^{-1}$

Answer and misconceptions

Option A: $9.9 \times 10^{3}$ ✗
Compares only the first numbersSees 9.9 as biggest but ignores the power of 10.

Option B: $2.1 \times 10^{4}$ ✓ Correct

Option C: $1.5 \times 10^{-5}$ ✗
Ignores the sign of the indexTreats 10⁻⁵ as bigger than 10⁴ because 5 > 4.

Option D: $21\,000 \times 10^{-1}$ ✗
Judges size by how long the number looks21 000 × 10⁻¹ is only 2100.
sf-05 Present from here

Work out $(3 \times 10^{4}) \times (2 \times 10^{5})$

Option A: $6 \times 10^{9}$

Option B: $6 \times 10^{20}$

Option C: $5 \times 10^{9}$

Option D: $6 \times 100^{9}$

Answer and misconceptions

Option A: $6 \times 10^{9}$ ✓ Correct

Option B: $6 \times 10^{20}$ ✗
Multiplies the powers of 1010⁴ × 10⁵ = 10⁹: add the indices.

Option C: $5 \times 10^{9}$ ✗
Adds the first numbers instead of multiplyingHas done 3 + 2 = 5.

Option D: $6 \times 100^{9}$ ✗
Multiplies the bases 10 × 10 as wellThe base stays 10; only the indices are added.