Write 6 × 10^42 × 10^-2 in standard form.

Worked solution for TMUA-P1-MNUM-042 is revealed on this page behind the solution details.

Why isn't the answer to TMUA-P1-MNUM-042 shown upfront?

The options are lettered without marking the correct one so you attempt TMUA-P1-MNUM-042 first — TMUA questions reward spotting the trap before you check the worked solution below.

Do I need a calculator for TMUA-P1-MNUM-042?

No — calculators are banned in the TMUA. TMUA-P1-MNUM-042 is set for a no-calculator target of about 150 seconds; the worked solution shows the fastest by-hand route.

Which TMUA specification point is TMUA-P1-MNUM-042?

TMUA-P1-MNUM-042 is Paper P1 · Number (specification code M-Num), level 2. Drill more of the same topic from this page.

TMUA-P1-MNUM-042 — Paper P1 · Number · Level 2

P1M-NumLevel 2~150s target

Spec: M-Num · No calculator · ~150s

Write

\dfrac{6 \times 10^4}{2 \times 10^{-2}}

in standard form.

Options

$3 \times 10^{6}$
$3 \times 10^{2}$
$4 \times 10^{6}$
$3 \times 10^{8}$
$12 \times 10^{2}$

Letters only — the answer key is hidden. Work it out, then check the solution below.

Hint (check trope)

No written hint yet — check the trope: mnum-standard-form, standard-form-calc, normalisation-trap. Name the trap first, work the stem by hand, then open the solution below.

Show solution

Divide the numbers:

6 / 2 = 3

. Subtract the powers:

10^{4 - (-2)} = 10^6

. So the answer is

3 \times 10^{6}

, already in standard form.
Trap:

3 \times 10^{2}

subtracts the powers the wrong way round (

4 - 2

instead of

4 - (-2)

Keep practising

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Keep practising

Same topic · same level

P1M-NumLevel 2

TMUA-P1-MNUM-005

What is the lowest common multiple (LCM) of 12, 18 and 20?

Number

Open TMUA-P1-MNUM-005 →

Same trap: standard-form-calc

P1M-NumLevel 2

TMUA-P1-MNUM-007

Write (4 × 10^5) × (3 × 10^-3) in standard form.

Number

Open TMUA-P1-MNUM-007 →

Step up a level

P1M-NumLevel 3

TMUA-P1-MNUM-011

4000 is invested. It grows by 5\% in year one, then falls by 5\% in year two. What is its final value?

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Open TMUA-P1-MNUM-011 →

TMUA-P1-MNUM-042 — Paper P1 · Number · Level 2

Options

Keep practising

Master Number

TMUA-P1-MNUM-042 — Paper P1 · Number · Level 2

Options

Keep practising

Master Number