The thickness of a layer of ice in a water body is 0.00205 m0.00205\ \text{m}.

  1. (a)

    Write 0.002050.00205 in standard form.

    Answer ...

  2. (b)

    The ice covers an area of 1.60×105 m21.60\times10^{5}\ \text{m}^2.

    Assuming that all the ice melts and ignoring the expansion of volume when water freezes, calculate the volume of water, in litres.

    Answer ... l

  3. (c)

    A thunderstorm occurs and rainwater is falling at an average rate of 5×10−15\times10^{-1} litres per second over the water body.

    Calculate the percentage increase in the volume of water in the water body after two hours.

    Answer ...%

Work through it with AI →

It won't just hand you the answer — it asks where you're stuck.How the checker works

Worked solution

13(a)

1. Rewrite the number with a coefficient between 1 and 10 and choose the correct power of 10.

0.00205=2.05×10−30.00205=2.05\times10^{-3}

The decimal point moves 3 places to the right to get 2.052.05, so the power is −3-3.

Answer

2.05×10−32.05\times10^{-3}

13(b)

1. Calculate the volume of ice/water in cubic metres.

Thickness =0.00205 m=2.05×10−3 m=0.00205\text{ m}=2.05\times10^{-3}\text{ m}

Volume=area×thickness\text{Volume}=\text{area}\times\text{thickness}

=(1.60×105)(2.05×10−3)=328 m3=(1.60\times10^5)(2.05\times10^{-3})=328\text{ m}^3

2. Convert the volume from cubic metres to litres.

Since 1 m3=1000 litres1\text{ m}^3=1000\text{ litres},

328 m3=328×1000=328000 litres328\text{ m}^3=328\times1000=328000\text{ litres}

Answer

410 l410\text{ l}

13(c)

1. Calculate the volume of rainwater added in two hours.

2 h=2×60×60=7200 s2\text{ h}=2\times60\times60=7200\text{ s}

Rainwater added
=5×10−1×7200=0.5×7200=3600 l=5\times10^{-1}\times7200=0.5\times7200=3600\text{ l}

2. Express the increase as a percentage of the original volume of water.

Original volume from part (b) =410 l=410\text{ l}.

Percentage increase
=3600410×100%=878.048…%=\frac{3600}{410}\times100\%=878.048\ldots\%
≈878%\approx878\%

Answer

878%878\%

AI analysis — may contain mistakes.

Worked this one out on paper? Snap your steps and Gigle's AI math checker will circle the step where it went wrong.

More questions on this topic

  1. 1近似数2.302.30万精确到___位,用科学记数法表示:___.
  2. 2A piece of wood which was 50 cm long, was in the shape of a uniform cylinder. A prism is cut out from the wood such that…
  3. 3中国是严重缺水的国家之一,人均淡水资源为世界人均水平的四分之一,所以我们要节约用水.若每人每天浪费水0.30.3升,则马鞍山全市230230万人每天浪费的水的总升数,用科学记数法表示为()(\quad) A. 6.9×1056.9×10^{5}…
  4. 4Mr Johnson has a plot of field that grows dandelion plants. An average of 70 dandelion plants grow on each square metre.…
  5. 5据报道,发射“天宫一号”的“长征二号”火箭的起飞质量约为493000kg.493000kg.数字493000493000用科学记数法表示为()(\quad) A. 49.3×10449.3×10^{4} B. 493×103493×10^{3} C. 4.93×1054.93×10^{5}…