Exam-Style Problems

Stage 9 - Q1 - 2 marks

18967

Insert the correct comparison sign.

\[1.1\times10^{2}\quad\square\quad1.3\times10^{2}\]

Hint

Compare coefficients when the powers are equal.

Stage 9 - Q2 - 2 marks

18968

Insert the correct comparison sign.

\[1.3\times10^{4}\quad\square\quad1.8\times10^{5}\]

Hint

First compare the exponents.

Stage 9 - Q3 - 3 marks

18969

Add. Give the result in standard form.

\[1.5\times10^{-3}+2.4\times10^{-3}\]

Hint

Treat the common power of ten as a common unit.

Stage 9 - Q4 - 3 marks

18970

Simplify into standard form.

\[(1.7\times10^{-1})\times10^{4}\]

Hint

Multiply powers of ten by adding their indices.

Stage 9 - Q5 - 4 marks

18971

Simplify into standard form.

\[(1.9\times10^{1})\div10^{2}\]

Hint

Division subtracts the exponent of the divisor.

Stage 9 - Q6 - 4 marks

18972

Simplify into standard form.

\[(2.1\times10^{3})\div10^{4}\]

Hint

Division subtracts the exponent of the divisor.

Stage 9 - Q7 - 5 marks

18973

Add and normalise your result.

\[2.3\times10^{-3}+1.3\times10^{-4}\]

Hint

Rewrite the first coefficient using the smaller power.

Stage 9 - Q8 - 5 marks

18974

2 identical strips each have length \(7.1\times10^{-5}\) metres. Find their total length in standard form.

Hint

The power of ten stays attached to the coefficient.

Stage 9 - Q9 - 5 marks

18975

A learner adds by adding both coefficients and exponents. Explain and correct the error.

\[2.7\times10^{0}+2.5\times10^{0}\]

Hint

Factor out the common power of ten.

Stage 9 - Q10 - 3 marks

18976

Three sensors measure lengths of \(4.8\times10^{-4}\) m, \(7.5\times10^{-5}\) m and \(1.25\times10^{-4}\) m. Find their total and how many equal parts of \(1.7\times10^{-5}\) m it contains.

Hint

Express all three measurements in units of ten to the power negative five.