Exam-Style Problems

Stage 9 - Q1 - 2 marks

19137

Calculate exactly.

\[11.8\times10^{3}\]

Hint

A negative power is a reciprocal.

Stage 9 - Q2 - 2 marks

19138

Calculate exactly.

\[12\times10^{-5}\]

Hint

A negative power is a reciprocal.

Stage 9 - Q3 - 3 marks

19139

Calculate exactly.

\[12.2\div10^{3}\]

Hint

A negative power is a reciprocal.

Stage 9 - Q4 - 3 marks

19140

Calculate exactly.

\[12.4\div10^{-5}\]

Hint

A negative power is a reciprocal.

Stage 9 - Q5 - 4 marks

19141

Find the integer exponent \(n\).

\[12.6\times10^n=0.0126\]

Hint

Compare the place values of corresponding digits.

Stage 9 - Q6 - 4 marks

19142

Find the integer exponent \(n\).

\[12.8\times10^n=0.000128\]

Hint

Compare the place values of corresponding digits.

Stage 9 - Q7 - 5 marks

19143

Find the integer exponent \(n\).

\[13\div10^n=13000\]

Hint

The output is larger, so the divisor is smaller than 1.

Stage 9 - Q8 - 5 marks

19144

Is multiplying every number by \(10^5\) guaranteed to increase its value? Test the given input.

\[x=-13.2\]

Hint

The word “every” includes negative numbers and zero.

Stage 9 - Q9 - 5 marks

19145

Calculate exactly.

\[(13.4\times10^{-3})\div10^{-3}\]

Hint

Subtract the negative divisor index.

Stage 9 - Q10 - 3 marks

19146

Find the integer \(n\) and verify by substitution.

\[\frac{0.0045\times10^n}{10^{-2}}=450\]

Hint

Combine the reciprocal power with the decimal coefficient first.