1 ESO - Unit 2 - Exercises 2.2 - Powers of 10

1. UNIT 02 October
1. Write the simplest numerals for each of the following:
a) ( 𝟖𝟖 ∙ 𝟏𝟏𝟏𝟏𝟏𝟏, 𝟎𝟎𝟎𝟎𝟎𝟎) + ( 𝟔𝟔 ∙ 𝟏𝟏𝟏𝟏, 𝟎𝟎𝟎𝟎𝟎𝟎) + ( 𝟐𝟐 ∙ 𝟏𝟏, 𝟎𝟎𝟎𝟎𝟎𝟎) + ( 𝟗𝟗 ∙ 𝟏𝟏𝟏𝟏𝟏𝟏) + ( 𝟓𝟓 ∙ 𝟏𝟏𝟏𝟏) + ( 𝟑𝟑 ∙ 𝟏𝟏) =
b) ( 𝟑𝟑 ∙ 𝟏𝟏, 𝟎𝟎𝟎𝟎𝟎𝟎, 𝟎𝟎𝟎𝟎𝟎𝟎) + ( 𝟓𝟓 ∙ 𝟏𝟏𝟏𝟏, 𝟎𝟎𝟎𝟎𝟎𝟎) + ( 𝟕𝟕 ∙ 𝟏𝟏𝟏𝟏𝟏𝟏) + ( 𝟗𝟗 ∙ 𝟏𝟏) =
c) ( 𝟐𝟐 ∙ 𝟏𝟏𝟏𝟏𝟕𝟕) + �𝟑𝟑 ∙ 𝟏𝟏𝟏𝟏𝟓𝟓� + ( 𝟔𝟔 ∙ 𝟏𝟏𝟏𝟏𝟒𝟒) + ( 𝟗𝟗 ∙ 𝟏𝟏𝟏𝟏𝟑𝟑) + ( 𝟔𝟔 ∙ 𝟏𝟏𝟏𝟏𝟏𝟏) + ( 𝟖𝟖 ∙ 𝟏𝟏) =
d) ( 𝟏𝟏𝟏𝟏𝟔𝟔) + ( 𝟏𝟏𝟏𝟏𝟒𝟒) + ( 𝟏𝟏𝟏𝟏𝟑𝟑) + ( 𝟏𝟏𝟏𝟏𝟐𝟐) + ( 𝟗𝟗 ∙ 𝟏𝟏𝟏𝟏𝟏𝟏) =
e) 𝟗𝟗 𝒕𝒕𝒕𝒕𝒕𝒕𝒕𝒕𝒕𝒕𝒕𝒕𝒕𝒕𝒕𝒕𝒕𝒕 𝒂𝒂𝒂𝒂𝒂𝒂 𝟖𝟖 𝒉𝒉𝒉𝒉𝒉𝒉𝒉𝒉𝒉𝒉𝒉𝒉𝒉𝒉𝒉𝒉 𝒂𝒂𝒂𝒂𝒂𝒂 𝟑𝟑 𝒕𝒕𝒕𝒕𝒕𝒕𝒕𝒕 𝒂𝒂𝒂𝒂𝒂𝒂 𝟔𝟔 𝒖𝒖𝒖𝒖𝒖𝒖𝒖𝒖𝒖𝒖 =
f) 𝟖𝟖 𝒉𝒉𝒉𝒉𝒉𝒉𝒉𝒉𝒉𝒉𝒉𝒉𝒉𝒉 𝒕𝒕𝒕𝒕𝒕𝒕𝒕𝒕𝒕𝒕𝒕𝒕𝒕𝒕𝒕𝒕𝒕𝒕 + 𝟗𝟗 𝒕𝒕𝒕𝒕𝒕𝒕 𝒕𝒕𝒕𝒕𝒕𝒕𝒕𝒕𝒕𝒕𝒕𝒕𝒕𝒕𝒕𝒕𝒕𝒕 + 𝟔𝟔 𝒉𝒉𝒉𝒉𝒉𝒉𝒉𝒉𝒉𝒉𝒉𝒉𝒉𝒉𝒉𝒉 +
𝟑𝟑 𝒕𝒕𝒕𝒕𝒕𝒕𝒕𝒕 𝒂𝒂𝒂𝒂𝒂𝒂 𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔 𝒖𝒖𝒖𝒖𝒖𝒖𝒖𝒖𝒖𝒖 =
g) 𝟓𝟓 𝒕𝒕𝒕𝒕𝒕𝒕 𝒎𝒎𝒎𝒎𝒎𝒎𝒎𝒎𝒎𝒎𝒎𝒎𝒎𝒎𝒎𝒎 + 𝟖𝟖 𝒉𝒉𝒉𝒉𝒉𝒉𝒉𝒉𝒉𝒉𝒉𝒉𝒉𝒉 𝒕𝒕𝒕𝒕𝒕𝒕𝒕𝒕𝒕𝒕𝒕𝒕𝒕𝒕𝒕𝒕𝒕𝒕 + 𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔 𝒕𝒕𝒕𝒕𝒕𝒕 𝒕𝒕𝒕𝒕𝒕𝒕𝒕𝒕𝒕𝒕𝒕𝒕𝒕𝒕𝒕𝒕𝒕𝒕 +
𝟓𝟓 𝒕𝒕𝒕𝒕𝒕𝒕𝒕𝒕𝒕𝒕𝒕𝒕𝒕𝒕𝒕𝒕𝒕𝒕 =
2. Write these numbers using expanded notation:
a) 𝟗𝟗, 𝟕𝟕𝟕𝟕𝟕𝟕 =
b) 𝟐𝟐𝟐𝟐, 𝟕𝟕𝟕𝟕𝟕𝟕 =
c) 𝟒𝟒𝟒𝟒, 𝟒𝟒𝟒𝟒𝟒𝟒 =
d) 𝟔𝟔𝟔𝟔𝟔𝟔, 𝟗𝟗𝟗𝟗𝟗𝟗 =
e) 𝟖𝟖𝟖𝟖𝟖𝟖, 𝟖𝟖𝟖𝟖𝟖𝟖 =
f) 𝟏𝟏, 𝟐𝟐𝟐𝟐𝟐𝟐, 𝟎𝟎𝟎𝟎𝟎𝟎 =
g) 𝟒𝟒𝟒𝟒, 𝟕𝟕𝟕𝟕𝟕𝟕, 𝟒𝟒𝟒𝟒𝟒𝟒 =
h) 𝟔𝟔, 𝟕𝟕𝟕𝟕𝟕𝟕, 𝟕𝟕𝟕𝟕𝟕𝟕 =
3. Expand these numbers using power notation:
a) 𝟗𝟗, 𝟕𝟕𝟕𝟕𝟕𝟕 =
b) 𝟐𝟐𝟐𝟐, 𝟕𝟕𝟕𝟕𝟕𝟕 =
c) 𝟒𝟒𝟒𝟒, 𝟒𝟒𝟒𝟒𝟒𝟒 =
d) 𝟔𝟔𝟔𝟔𝟔𝟔, 𝟗𝟗𝟗𝟗𝟗𝟗 =
Axel Cotón Gutiérrez Mathematics 1º ESO Exercises – 1.2.2.1

2. UNIT 02 October
e) 𝟖𝟖𝟖𝟖𝟖𝟖, 𝟖𝟖𝟖𝟖𝟖𝟖 =
f) 𝟏𝟏, 𝟐𝟐𝟐𝟐𝟐𝟐, 𝟎𝟎𝟎𝟎𝟎𝟎 =
g) 𝟒𝟒𝟒𝟒, 𝟕𝟕𝟕𝟕𝟕𝟕, 𝟒𝟒𝟒𝟒𝟒𝟒 =
h) 𝟔𝟔, 𝟕𝟕𝟕𝟕𝟕𝟕, 𝟕𝟕𝟕𝟕𝟕𝟕 =
4. Write as a power of 10:
a) 𝟏𝟏𝟏𝟏𝟏𝟏 =
b) 𝟏𝟏, 𝟎𝟎𝟎𝟎𝟎𝟎 =
c) 𝟏𝟏𝟏𝟏, 𝟎𝟎𝟎𝟎𝟎𝟎 =
d) 𝒐𝒐𝒐𝒐𝒐𝒐 𝒎𝒎𝒎𝒎𝒎𝒎𝒎𝒎𝒎𝒎𝒎𝒎𝒎𝒎 =
e) 𝒐𝒐𝒐𝒐𝒐𝒐 𝒃𝒃𝒃𝒃𝒃𝒃𝒃𝒃𝒃𝒃𝒃𝒃𝒃𝒃 =
f) 𝒐𝒐𝒐𝒐𝒐𝒐 𝒕𝒕𝒕𝒕𝒕𝒕𝒕𝒕𝒕𝒕𝒕𝒕𝒕𝒕𝒕𝒕 =
5. Find:
6. Find:
Axel Cotón Gutiérrez Mathematics 1º ESO Exercises – 1.2.2.2

3. UNIT 02 October
7. How long would a satellite orbiting the earth at 8,000 km per hour take to fly 1 million
km?
8. A fighter jet travels at 1,000 km per hour. How long will it take the jet to fly non-stop
for 1,000,000 km?
9. How long would a car, travelling non-stop at 100 kilometres per hour, take to travel a
million kilometres?
Axel Cotón Gutiérrez Mathematics 1º ESO Exercises – 1.2.2.3

4. UNIT 02 October
10. A sporting ground has a capacity of 50,000 people. How many capacity crowds would
be needed so that 1,000,000 people will have visited the ground?
11. Express in standard form the following numbers:
a) 𝟒𝟒, 𝟎𝟎𝟎𝟎𝟎𝟎, 𝟎𝟎𝟎𝟎𝟎𝟎, 𝟎𝟎𝟎𝟎𝟎𝟎 =
b) 𝟑𝟑𝟑𝟑𝟑𝟑, 𝟔𝟔𝟔𝟔𝟔𝟔, 𝟎𝟎𝟎𝟎𝟎𝟎 ( 𝒓𝒓𝒓𝒓𝒓𝒓𝒓𝒓𝒓𝒓 𝒕𝒕𝒕𝒕 𝒕𝒕𝒕𝒕𝒕𝒕 𝒎𝒎𝒎𝒎𝒎𝒎𝒎𝒎𝒎𝒎𝒎𝒎𝒎𝒎) =
c) 𝒏𝒏𝒏𝒏𝒏𝒏𝒏𝒏𝒏𝒏𝒏𝒏 𝒐𝒐𝒐𝒐 𝒆𝒆𝒆𝒆𝒆𝒆𝒆𝒆𝒆𝒆𝒆𝒆𝒆𝒆𝒆𝒆𝒆𝒆𝒆𝒆 𝒎𝒎𝒎𝒎𝒎𝒎𝒎𝒎𝒎𝒎𝒎𝒎𝒎𝒎𝒎𝒎𝒎𝒎 𝒊𝒊𝒊𝒊 𝒐𝒐𝒐𝒐𝒐𝒐 𝒘𝒘𝒘𝒘𝒘𝒘𝒘𝒘𝒘𝒘 𝒍𝒍𝒍𝒍𝒍𝒍𝒍𝒍𝒍𝒍:
𝟑𝟑𝟑𝟑𝟑𝟑, 𝟑𝟑𝟑𝟑𝟑𝟑, 𝟎𝟎𝟎𝟎𝟎𝟎, 𝟎𝟎𝟎𝟎𝟎𝟎, 𝟎𝟎𝟎𝟎𝟎𝟎, 𝟎𝟎𝟎𝟎𝟎𝟎, 𝟎𝟎𝟎𝟎𝟎𝟎, 𝟎𝟎𝟎𝟎𝟎𝟎 =
d) 𝒐𝒐𝒐𝒐𝒐𝒐 𝒈𝒈𝒈𝒈𝒈𝒈𝒈𝒈 𝒐𝒐𝒐𝒐 𝒐𝒐𝒐𝒐𝒐𝒐𝒐𝒐𝒐𝒐𝒐𝒐 𝒄𝒄𝒄𝒄𝒄𝒄𝒄𝒄𝒄𝒄𝒄𝒄𝒄𝒄𝒄𝒄 𝟑𝟑𝟑𝟑, 𝟔𝟔𝟔𝟔𝟔𝟔, 𝟑𝟑𝟑𝟑𝟑𝟑, 𝟎𝟎𝟎𝟎𝟎𝟎, 𝟎𝟎𝟎𝟎𝟎𝟎, 𝟎𝟎𝟎𝟎𝟎𝟎, 𝟎𝟎𝟎𝟎𝟎𝟎, 𝟎𝟎𝟎𝟎𝟎𝟎 𝒂𝒂𝒂𝒂𝒂𝒂𝒂𝒂𝒂𝒂 =
12. Find the x value:
a) 𝟐𝟐, 𝟗𝟗𝟗𝟗𝟗𝟗, 𝟒𝟒𝟒𝟒𝟒𝟒 ≈ 𝟐𝟐𝟐𝟐 ∙ 𝟏𝟏𝟏𝟏𝒙𝒙
b) 𝟑𝟑, 𝟔𝟔𝟔𝟔𝟔𝟔, 𝟐𝟐𝟐𝟐𝟐𝟐, 𝟖𝟖𝟖𝟖𝟖𝟖 ≈ 𝟑𝟑𝟑𝟑 ∙ 𝟏𝟏𝟏𝟏𝒙𝒙
c) 𝟏𝟏𝟏𝟏, 𝟓𝟓𝟓𝟓𝟓𝟓, 𝟎𝟎𝟎𝟎𝟎𝟎, 𝟎𝟎𝟎𝟎𝟎𝟎, 𝟎𝟎𝟎𝟎𝟎𝟎 ≈ 𝟐𝟐𝟐𝟐 ∙ 𝟏𝟏𝟏𝟏𝒙𝒙
Axel Cotón Gutiérrez Mathematics 1º ESO Exercises – 1.2.2.4