Conversion of units and scientific notation

Sometimes, the result of an operation on a calculator is a very large or very small number, and it is not always viable to use multiples or submultiples to express it.

Scientific notation is a way of writing numbers that makes them easier to read and understand.

Scientific notation is a way of writing large numbers using
integers, decimals and powers of ten.

The Orion nebula is 1,270 light years away. To express this in other units
it is best to use scientific notation:

1.2 · 10¹⁶ km

Write the following numbers using scientific notation:

a) 346,000

b) 0.000064

We are going to draw a table with a column for each number:

	a	b
1. Look at the original number.	346,000	0.000064
2. Write the first digit other than zero, then a decimal point followed by the remaining digits. Don’t write the zeros to the right of the decimal point.	3.46	6.4
3. Write the power of ten (10^x). Count how many places you have to move the decimal point until you only have one integer left. This is the exponent that you will use.	$3 4 con paréntesis de arriba encima pila 6 coma con paréntesis de arriba encima 0 con paréntesis de arriba encima 0 con paréntesis de arriba encima 0 con paréntesis de arriba encima flecha derecha negrita 3 negrita. negrita 46 negrita por negrita 10 elevado a negrita 5$ If the number was bigger than one, the power will be positive.	$0.0 con paréntesis de arriba encima 0 con paréntesis de arriba encima 0 con paréntesis de arriba encima 6 con paréntesis de arriba encima 4 flecha derecha negrita 6 negrita. negrita 4 negrita por negrita 10 elevado a negrita menos negrita 5 fin elevado$ If the number was smaller than one, the power will be negative.

Convert these amounts and fill the blanks.

0.0062 g → mg

167 g → kg

0.05 m²→ cm²

30 mL → L

0.3 L → cm³

Match each time unit to its corresponding equivalent.

15 min
1 h 30 min
1 day
1 year
1 month (30 days)
3,600 s
1 week

86,400 s
1 h
90 min
31,536,000 s
720 h
10,080 min
0.25 h

Write, with all its digits, the following numbers written in scientific notation.

Help: Write numbers without blanks and remember to use a dot (decimal point) for decimals.

2.705 · 10²→

1.075 · 10^–⁴→

3.05 · 10⁶→

4.06 · 10^–6→

3.99 · 10⁹→

7.0002 · 10^–5→

A football player kicks the ball for a penalty kick. The ball reaches a speed of 34 m/s. What's the speed in km/h?

(0 words)

The air in a room has a density of 1,225, expressed in SI units.

Now, express the density in g/L.

(0 words)

Light travels at 300,000 km/s. Calculate its speed in m/h and express the result in scientific notation.

(0 words)

A garden snail moves at 14 mm/s. Calculate its speed in km/h and express it in scientific notation.

(0 words)

,
You have completed the lesson!

Below is the time you have spent on the activity and the score you obtained.

Time spent

Score

How can we help you?

Couldn't find what you were looking for?

Please describe the issue you are experiencing and provide as many details as possible. Let us know the book, class, access device, licence code, username, used browser or if it occcurs in our app:

Unit converter

Scientific notation

How far is Orion?

Let's see an example

Write the following numbers using scientific notation:

a) 346,000

b) 0.000064

1. Look at the original number.

Activities

Converting units

Convert these amounts and fill the blanks.

Time units

Match each time unit to its corresponding equivalent.

Scientific notation

Write, with all its digits, the following numbers written in scientific notation.

Help: Write numbers without blanks and remember to use a dot (decimal point) for decimals.

Kick the ball!

A football player kicks the ball for a penalty kick. The ball reaches a speed of 34 m/s. What's the speed in km/h?

Density units

Speed of light

Light travels at 300,000 km/s. Calculate its speed in m/h and express the result in scientific notation.

At a snail's speed

A garden snail moves at 14 mm/s. Calculate its speed in km/h and express it in scientific notation.

Now I know