David Weber, Talei Kunkel, Rose Harrison and, Fatima Remtulla Solutions for Chapter: Number Discoveries and Developments, Exercise 17: Practice 2

Order the quantities in each set of four from lowest to highest. Show your working

$2^{-2}, 3^{-1}, {\left(\frac{1}{4}\right)}^{-1}, {\left(\frac{5}{8}\right)}^0$

Order the quantities in each set of four from lowest to highest. Show your working

$7^{-1}, 2^{-2}, 1^{-3}, {\left(\frac{2}{5}\right)}^2$

Order the quantities in each set of four from lowest to highest. Show your working

$1^0,3^{-1},0^1,{\left(\frac{1}{2}\right)}^2$

Ricardo says:" $5^0$ equals zero because you have zero $5$s, which means you don't have anything. You have zero." Explain any faults in his thinking.
 

Talei says: "Negative exponents make fractions. If the negative exponent is already in the denominator of a fraction, then it makes an integer." Is Talei correct? Explain.

 

Anna says:"$8\frac{1}{2}$ must be $4$ since you have half of $8$. "Explain why this thinking is faulty.
 

Thomas states: "A positive exponent is the number of times you multiply the base. A negative exponent is the number of times you divide by the base. "Do you agree? Explain your answer.
 

The development of the current metric system of units began in France in the 18th century. Basic units for measurements like angles, lengths, mass, and capacity were created, often derived from the properties of natural objects such as water. For example, $1$ liter of water has a mass of $1$kg. Multiples or divisions of these units could be created by using prefixes, such as those used in the units millimetre and kilogram. Some of the prefixes are given in the table below. Copy and complete the table.