Scientific Notation

Hey there, math whiz! Imagine you're on an exciting science adventure with Olivia and Henry. A positive exponent in scientific notation is like a magical guide that tells you how many places the decimal moves to the ____________. Can you help them solve this mystery?

Answer explanation

In scientific notation, a positive exponent indicates how many places the decimal moves to the right. This means the number becomes larger, confirming that the correct answer is 'right'.

Hey Amelia and Aarav, did you know that a negative exponent in scientific notation is like a magical spell that tells you how many places the decimal dances to the ____________?

Answer explanation

A negative exponent in scientific notation indicates how many places to move the decimal to the left. This means the correct answer is 'left', as it shows a decrease in value.

Join Daniel and Charlotte on their exciting space mission! Can you help them discover how to express 6,400,000 in scientific notation?

• 6.4 × 10⁶

• 6.4 × 10⁵

• 64 × 10⁵

• 6.4 × 10⁷

Answer explanation

To convert 6,400,000 to scientific notation, move the decimal point 6 places to the left, resulting in 6.4. Thus, it is expressed as 6.4 × 10⁶, making this the correct choice.

Join Chloe, Emma, and Mia on their exciting adventure through the world of numbers! Can you help them discover the scientific notation for 0.00052?

• 5.2 × 10⁻⁴

• 5.2 × 10⁻³

• 52 × 10⁻⁴

• 0.52 × 10⁻⁴

Answer explanation

To convert 0.00052 to scientific notation, move the decimal point 4 places to the right, giving 5.2. Thus, it becomes 5.2 × 10⁻⁴, which is the correct choice.

Match the following numbers with their decimal notation.

• 7.1 × 10⁴

• 71000

• 7.1 × 10³

• 7100

• 7.1 × 10¹

• 0.71

• 7.1 × 10⁻¹

• 71

Answer explanation

To convert 7.1 × 10⁴ to decimal notation, move the decimal point 4 places to the right, resulting in 71000. Thus, the correct answer is 71000.

Match the following scientific notations with their decimal equivalents.

• 4.5 × 10⁻¹

• 0.45

• 4.5 × 10⁻²

• 0.045

• 4.5 × 10⁰

• 4.5

• 4.5 × 10⁻³

• 0.0045

Answer explanation

To convert 4.5 × 10⁻³ to decimal, move the decimal point 3 places to the left. This gives 0.0045, which is the correct answer.

Hey math wizards! Thomas, Neha, and Alexander are having a lively debate about the magical world of scientific notation. Can you join their fun and help them figure out which of the following numbers (a)   is written in proper scientific notation?

• 3.2 × 10²
• 32 × 10¹
• 0.32 × 10²
• 320 × 10⁰

Answer explanation

The number in proper scientific notation must have a coefficient between 1 and 10. 3.2 × 10² meets this criterion, while the others do not, as they either exceed 10 or are less than 1.

Hey Scarlett, did you know that scientific notation is like a superhero for numbers, swooping in to save the day by helping us represent both colossal and minuscule numbers? (a)  

• True

• False

Answer explanation

True. Scientific notation simplifies the representation of very large or very small numbers, making them easier to read and work with, just like a superhero makes complex situations manageable.

Lily and Owen are having a friendly math challenge! Lily bets Owen that he can't convert 0.000089 into scientific notation. Can you help Owen fill in the blank? (a)  

• 8.9 × 10⁻⁵

• 8.9 × 10⁵

• 89 × 10⁻⁶

• 0.89 × 10⁻⁴

Answer explanation

To convert 0.000089 to scientific notation, move the decimal point 5 places to the right, giving 8.9. This results in 8.9 × 10⁻⁵, which is the correct scientific notation for the number.

Addison and Eesha are having a friendly chat about their dream savings. Addison wonders, "If I had 2.5 million dollars, how would that look in decimal notation?" Can you help Eesha figure out the right answer?

• 250,000

• 2,500,000

• 25,000

• 250

Answer explanation

2.5 million dollars in decimal notation is written as 2,500,000. This is because 2.5 million equals 2,500,000 when converted from millions to the standard decimal format.