This document contains math word problems and exercises involving operations with large numbers written in standard, expanded, and exponential forms. It asks students to perform calculations such as adding and multiplying large numbers, converting between forms, finding time and distance using rates, and expressing very large numbers in standard scientific notation.

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