Question

c) ( 3.5 \times 10^{-3} ) __________
d) ( 1.08 \times 10^{-7} ) __________
review! which number sets does ( 5.8 \times 10^4 ) belong to? write the number in expanded form, then circle all that apply: __________
natural whole integer rational irrational

Explanation:

Part c: Converting \( 3.5 \times 10^{-3} \) to Standard Form

Step 1: Recall the rule for negative exponents

A negative exponent in scientific notation means we move the decimal point to the left. For \( 10^{-n} \), we move the decimal \( n \) places to the left. Here, \( n = 3 \).

Step 2: Move the decimal point

Starting with \( 3.5 \), moving the decimal point 3 places to the left: \( 3.5 \times 10^{-3}= 0.0035 \)

Part d: Converting \( 1.08 \times 10^{-7} \) to Standard Form

Step 1: Recall the rule for negative exponents

For \( 10^{-n} \), move the decimal \( n \) places to the left. Here, \( n = 7 \).

Step 2: Move the decimal point

Starting with \( 1.08 \), moving the decimal point 7 places to the left: \( 1.08 \times 10^{-7}= 0.000000108 \)

REVIEW: Analyzing \( 5.8 \times 10^{4} \)

Step 1: Expand the number

First, convert \( 5.8 \times 10^{4} \) to standard form. \( 10^{4}=10000 \), so \( 5.8 \times 10000 = 58000 \)

Step 2: Identify number sets

• Natural Numbers: Counting numbers (1, 2, 3, ...). 58000 is a natural number.
• Whole Numbers: Natural numbers plus 0. 58000 is a whole number.
• Integers: Whole numbers and their negatives. 58000 is an integer.
• Rational Numbers: Numbers that can be expressed as a fraction \( \frac{a}{b} \) ( \( b

eq0 \) ). 58000 can be written as \( \frac{58000}{1} \), so it is rational.

• Irrational Numbers: Numbers that cannot be expressed as a fraction (e.g., \( \sqrt{2} \), \( \pi \) ). 58000 is not irrational.

Answer:

s:

• c) \( 0.0035 \)
• d) \( 0.000000108 \)
• REVIEW: Expanded form: \( 58000 \); Number sets: Natural, Whole, Integer, Rational