Question

solve. 9. math journal using different number words, write three pairs of equivalent very large and very small equivalent numbers. for example, 1 billion is equivalent to 1000 million. then write three pairs of equivalent very large and very small equivalent numbers. use decimals in at least two of your number pairs. 10. a virus measures 250 billionths of a metre. a bacterium measures 45 millionths of a metre. which is larger? how many times larger is it than the other? 11. the distance between earth and the sun is about 150 million kilometres. the distance between earth and uranus is about 2.7 billion kilometres. which distance is greater? how many times greater is it?

Explanation:

9

Step1: Recall equivalent large - number pairs

1 billion = 1000 million, 1 trillion = 1000 billion, 1 quadrillion = 1000 trillion.

Step2: Write three pairs

1. 1 billion = 1000 million. In decimal form, 1.0 billion = 1000.0 million.
2. 1 trillion = 1000000 million. In decimal form, 1.0 trillion = 1000000.0 million.
3. 1 quadrillion = 1000000000 million. In decimal form, 1.0 quadrillion = 1000000000.0 million.

Step1: Compare the sizes

250 billionths = 0.000000250 and 45 millionths = 0.000045. Since 0.000045>0.000000250, the bacterium's size (45 millionths of a metre) is larger.

Step2: Calculate the ratio

Let \(a = 0.000045\) and \(b=0.000000250\). The ratio \(\frac{a}{b}=\frac{0.000045}{0.000000250}=\frac{45000}{250} = 180\).

Step1: Identify the distances

Distance from Earth - Sun: \(d_1 = 150\times10^{6}\) km. Distance from Earth - Uranus: \(d_2=2.7\times 10^{9}\) km.

Step2: Compare the distances

Since \(2.7\times 10^{9}>150\times 10^{6}\), the distance between Earth and Uranus is greater.

Step3: Calculate the ratio

\(\frac{d_2}{d_1}=\frac{2.7\times 10^{9}}{150\times 10^{6}}=\frac{2.7\times10^{9}}{1.5\times10^{2}\times10^{6}}=\frac{2.7}{1.5}\times10^{9-(2 + 6)} = 1.8\times10^{1}=18\).

Answer:

1. 1 billion = 1000 million
2. 1 trillion = 1000000 million
3. 1 quadrillion = 1000000000 million

10