Sovi.AI - AI Math Tutor

Scan to solve math questions
ENFRDEESJAZH-CNZH-TW

QUESTION IMAGE

c) $3.5 \\times 10^{-3}$ __________ d) $1.08 \\times 10^{-7}$ _________…

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: __________

Explanation:

Response
Part c: Converting \( 3.5 \times 10^{-3} \) to standard form

Step 1: Understand negative exponent

A negative exponent \( 10^{-n} \) means we divide by \( 10^n \), or move the decimal point \( n \) places to the left. Here, \( n = 3 \).

Step 2: Move decimal point

Start with \( 3.5 \). Moving the decimal point 3 places to the left: first place left gives \( 0.35 \), second gives \( 0.035 \), third gives \( 0.0035 \).
So, \( 3.5 \times 10^{-3} = 0.0035 \).

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

Step 1: Understand negative exponent

For \( 10^{-7} \), we move the decimal point 7 places to the left.

Step 2: Move decimal point

Start with \( 1.08 \). Moving the decimal 7 places left: after moving 1 place left: \( 0.108 \), 2: \( 0.0108 \), 3: \( 0.00108 \), 4: \( 0.000108 \), 5: \( 0.0000108 \), 6: \( 0.00000108 \), 7: \( 0.000000108 \).
So, \( 1.08 \times 10^{-7} = 0.000000108 \).

REVIEW: \( 5.8 \times 10^4 \)

Step 1: Expand \( 5.8 \times 10^4 \)

\( 10^4 = 10000 \), so \( 5.8 \times 10000 = 58000 \). In expanded form (place value): \( 5 \times 10000 + 8 \times 1000 + 0 \times 100 + 0 \times 10 + 0 \times 1 = 50000 + 8000 \).

Step 2: Identify number sets

\( 5.8 \times 10^4 = 58000 \), which is a positive integer, so it belongs to:

  • Natural Numbers (counting numbers, if we consider positive integers),
  • Whole Numbers (natural numbers + 0),
  • Integers (positive/negative whole numbers),
  • Rational Numbers (can be written as a fraction, \( \frac{58000}{1} \)),
  • Real Numbers (all rational/irrational numbers).

Answer:

s:

  • c) \( \boldsymbol{0.0035} \)
  • d) \( \boldsymbol{0.000000108} \)
  • REVIEW: Expanded form: \( \boldsymbol{58000} \) (or \( 5 \times 10^4 + 8 \times 10^3 \)); Number sets: Natural Numbers, Whole Numbers, Integers, Rational Numbers, Real Numbers (circle these).