Students use the place value to multiply and divide by decimal numbers and round numbers to the required significant digits. As they learn, they apply this knowledge to evaluate numbers written using standard indexing formats.

This unit takes place in Semester 8 and continues with Fractions, Decimals, and Percentages.

**Lessons in indicators and approximations**

4 part lesson

##### Multiply and divide numbers by 0.1 and 0.01

4 part lesson

##### Round a number to significant digits

4 part lesson

##### Create Approximation Using Rounding

4 part lesson

##### Simplification of numbers written in exponential form

4 part lesson

##### negative exponent

4 part lesson

##### large numbers in normal form

4 part lesson

##### write small numbers in normal form

**Other resources**

augmented learning

##### Standard form – few

augmented learning

##### guess the solution

augmented learning

##### Index rule

augmented learning

##### Standard form – many

problem solving

##### Working with standard forms

problem solving

##### Quote

**prerequisite knowledge**

- Understand and use arbitrarily sized decimals, measurements, and integer digit values
- It uses four operations with formal notations that apply to integers and decimals.
- Sort positive and negative integers, decimals, and fractions. Use the number line as a model for the ordering of real numbers. =, ≠,<、>Use the symbols , ≤, ≥

**key concepts**

- 2
^{3}, where 2 is the base and 3 is the power. Raise the base to power. - Students should understand that dividing by a decimal and multiplying by a reciprocal are equivalent. Because this leads to dividing by a fraction.
- All powers of zero are equal to one. Students need to understand this that a number divided by itself is equal to 1.
- The multiplication rule can be defined as n
^{a}×n^{b}= n^{(a+b)}. The splitting rule is defined as n.^{a}÷n^{b}= n^{(ab)}. - power rule (2
^{3})^{2}= 2^{6}An extension of the multiplication rule. The power-of-zero rule is an extension of the division rule. - A number raised to the negative power of one is the reciprocal of that number.
- When rounding 3.5 to one significant digit, 3 is the most significant and 1/5 rounds up to 4.
- If you write the number with the standard index of the number before the decimal point, it must be in the range 1 to 9.

**work mathematically**

develop fluency

- Choose and use appropriate calculation methods to solve increasingly complex problems.

justify mathematically

- Extends and formalizes knowledge of ratios and ratios in dealing with measures and geometry and formulating proportional relationships algebraically.
- Make and test guesses about patterns and relationships. Look for proofs and counterexamples.

problem solving

- Develop the use of formal mathematical knowledge to interpret and solve problems.

**Subject content**

number

- Use conventional notation for arithmetic precedence, such as parentheses, powers, roots, and reciprocals.
- Uses integer powers and related real roots (square, cubic, and higher) and recognizes powers of 2, 3, 4, and 5
- Interpret and compare numbers in normal form A × 10
^{n}where 1≤A<10 and n is a positive or negative integer or zero - Round numbers and measurements to the appropriate precision [for

example, to a number of decimal places or significant figures] - Estimate the answer using rounding approximation and write the inequality notation a
- Accurately calculate and properly interpret results using calculators and other techniques

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